Saturday

April 18, 2015

April 18, 2015

Number of results: 103,911

**functions**

For each problem, construct two composite functions, . Evaluate each composite function for x=2 ok i have not dealt with composite functions can I please get some help with this as I have 20 questions to do can someone show me step by step on how to properly solve this ...
*October 18, 2013 by Johnathan*

**Composite Functions**

Find the composite functions for the given functions. (6 marks) f(x) = 4x + 1 and g(x) = x2 f(x) = sin x and g(x) = x2 - x + 1 f(x) = 10x and g(x) = log x
*January 19, 2013 by Anonymous*

**algebra functions**

construct two composite functions, Evaluate each composite function for x=2. i do not fully understand functions yet can someone explain and show me what to do step by step f(x)=x+1 g(x)=x-2
*October 16, 2013 by tani*

**algebra functions**

can someone please check my answer For each problem, construct two composite functions, . Evaluate each composite function for x=2 f(x)=3x g(x)=1/x f(g)*(x)=3x(1)/x x=2 3x(1)/x=6 g(f)*(x)=(3x)=2*3x=6 x=2 3*(2)=6*6=36
*October 17, 2013 by tani*

**algebra functions check my answer**

For each problem, construct two composite functions, . Evaluate each composite function for x=2 f(x)=3x g(x)=1/x f(g)*(x)=3x(1)/x x=2 3x(1)/x=6 g(f)*(x)=(3x)=2*3x=6 x=2 3*(2)=6*6=36
*October 17, 2013 by tani*

**math**

how to you find a composite function form of y in this problem? y = 1/[(x^2+3x-5)^3] I dont understand your question. Composite functions require two functions. You listed one. Please amplify. That's what I thought at first. But I am thinking I might need to substitute y in ...
*June 19, 2006 by greg*

**algebra functions**

can someone help me with this and explain it to me step by step so i can try to solve the remaining problems i have I have no idea of what I am supposed to do For each problem, construct two composite functions, . Evaluate each composite function for x=2. f(x)=x^2: g(x)=x-1/x
*October 16, 2013 by Ricki*

**Functions**

consider the functions g(x)=(4-x^2)^0.5 and h(x)=(x^2)-5. find the composite functions hog(x) and goh(x), if they exist, and state the domain and range of the composite functions. ------------------------------ ok, i have figured out that hog(x)=-1-X^2, but in my answer ...
*May 17, 2008 by Ann*

**Math ( composite functions )**

I need some help with composite functions where i have to find the f(g(x)) and g(f(x)) on most of them I just couldn't figure out how to multiply.... 1) f(x) = ³√x-5 , g(x) = x^3 + 1 So I started on this one and i got confused with the cubed f(g(x))=³√(x^3+1)-5 ...
*October 2, 2012 by Mira*

**Calculus**

Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 - x + 1 f(x) = 10^x and g(x) = log x If f = {(-2...
*September 2, 2013 by Britt*

**composite functions**

f(x)=2x-4, g(x)=x squared + 5x What is F o G and Domain Okay, we are given f and g as functions of x. To compose a function means to use one function, g in this case, as the argument of the other, f in this case. Thus we want f o g = f(g(x)) With f(x) = 2x-4 and g(x) = x^2 + ...
*July 6, 2006 by Anonymous*

**Math (Grade 12)**

I need help with this problem (composite functions): If f(x) = 4x-3 and h(x )= 4x^2-21, find a function g such that f(g(x)) = h. I don't understand how we're supposed to combine the functions. Oh, and the answer is supposed to be g(x) = x^2 - (9/2). Thanks!
*September 17, 2008 by Lucy*

**Functions**

I have to find the domain and range for the composite of functions G(x)=sinx and h(x)=x^2-x+1. I'm confused about this and would really appreciate some help. Thanks.
*September 24, 2010 by Sarah*

**math**

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...
*February 10, 2013 by Julia*

**calculus**

when working with composite functions, does fog=gof? how do i create two functions,f(x) and g(x) to show that this statement is either true or false.i need to expain my reasoning
*October 19, 2011 by ayotal*

**Precalculus **

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the...
*February 10, 2013 by Julie*

**Math (Composite Functions)**

I don't understand this question at all. If f(x) = 4x - 3 and h(x) = 4x^2 - 21, find a function g such that f ͦ g = h.
*September 8, 2008 by Lucy*

**Math**

Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United ...
*January 20, 2013 by Anonymous*

**Math**

Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United ...
*January 20, 2013 by Anonymous*

**Math**

I have to find the domain and range for the composite of functions G(x)=sinx and h(x)=x^2-x+1. I'm confused about this and would really appreciate some help. Thanks.
*September 24, 2010 by Sarah*

**math**

The number 5 is A) prime B) composite C) neither prime nor composite D) both prime and composite
*August 27, 2014 by pietro*

**Algebra**

Two functions f and g are defined by f:x = 25 /(3x-2) g:x = x^2 Find the composite function
*December 19, 2012 by Nikki*

**College Alegbra**

A new store opens in New York. You received a coupon for $5.00 off a pair of jeans j(x) = x-5. When you get to the store you learn that they are giving a 25% discount d(x)=.75x a) Write a composite function for the cost of the jeans if the 25% discount is applied after the $5....
*June 19, 2014 by Sheniqua*

**Math quick question**

"If f = {(-2,-1), (-1,2), (0,6), (1,3), (2,-1), (3,-5), (4,0), (5,8)} and g = {(-2,6), (-1,5), (0,-8), (1,3), (2,9), (3,9), (4,0), (5,-2)}, then find f composite g and g composite f."
*January 19, 2013 by Anonymous*

**Algaebra**

Two functions f and g are defined by f:x = 25 /(3x-2) g:x = x^2 Find the composite function Please show all calculations, thank you!
*December 19, 2012 by Samantha*

**math**

how would this equation look: y=f(x+3) when y=f(x)= x^2 would it look like so.... x^2(x+3) adam, there's a slight problem with your notation in the expression y = f(x+3). Ordinarily we wouldn't put an expression in place of a variable, unless we were making what is termed a ...
*July 6, 2006 by adam*

**Algebra**

give indicated composite for pair of functions (g o f)(x):f(x)=x-3/6, g(x)=6x+3 g(f(x)) g(x-3/6) =6*x-3+3/6 would my answer be: (g o f)(x)=x I am not sure if I answered the problem completely.
*March 27, 2008 by Larry*

**RE: Math Urgent**

I posted this earlier but I think I phrased it in a confusing way Find g(x) + g(x) if g(x) = {(-4,5), (-2,-3), (0,5), (1,3), (3,-1), (5,5)} and g(x) = {(-3,-2), (-2,6), (-1,0), (1,0), (2,-6), (3,5), (4,0), (6,-2)}. I don't need the whole thing done i'm just very confused on ...
*January 21, 2013 by Anonymous*

**math**

can some one please help me with the following questions as i dont understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the derivative of each of ...
*February 8, 2007 by hanny*

**Math Analysis**

6. Prove that f(x) = (3/4)x^4 + 2 and g(x) = (4sqrt(108x-216))/3 are inverses. I know you solve it with composite functions f(g(x)) and g(f(x)), and I solved f(g(x)), but I can't seem to solve g(f(x)) to equal x, like it should. Can someone show me how to solve this? Thanks :)
*October 24, 2009 by Emily*

**Math Analysis**

Let f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x. Express the following function k as a composite of three of these four functions. k(x)= sqrt (x^3 - 4) Do I need to factor anything out of the parentheses or something? If you can, please explain this problem to me :) any...
*October 14, 2009 by Emily*

**Math - Domain of Composite**

Find the domain of the composite function . Please show all of your work. f(x) = sqrt(x); g(x) = 2x + 12
*June 5, 2011 by Armando*

**math**

Can you explain to us if we have the functions c(t) = 3t + 2, where c is the cost in dollars of t hours of tutoring and t(m) = m2 - 1 where t is hours of tutoring and m is the number of minutes tutored, what the input and output values would be of the composite function c(t(m))?
*June 1, 2012 by Julie Hurley*

**ADVANCED FUNCTIONS**

What is the domain of the composite function of f(x)=x^2 and g(x)=sin x when (g o f)(x) and (f o g)(x)?? when i joined the two function it looks the same to me..
*June 10, 2013 by Anonymous*

**algebra2**

(1.06)(.7x) = .742x (1.06x)(.7) = .742x . how do you compare these composite functions?
*January 22, 2011 by jennifer*

**Math22 **

1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y= (g(x), f(u)) = 2. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ...
*October 7, 2014 by Anonymous*

**Algebra**

Let f(x) = 6/x-1 and g(x) = 1+3/x. Please fing the composite function. This is what i got so far. =f (1+3/x) =6/x-1 = =f (1+3/x) = 6/ [1+3/x - 1] How do I get the composite?
*June 24, 2009 by Stacy*

**Composite Functions**

f(x)=(7x+28)/(x-3) and g(x)=(3x+28)/(x-7) Find: (fog)(x) (gof)(x) (fog)(-1)
*December 3, 2011 by MV*

**Math - Domain of Composite function**

Find the domain of the composite function f ₒ g . Please show all of your work. f(x) = √x; g(x) = 2x + 12
*June 3, 2011 by CheezyReezy*

**math**

Cruz and his friend, Penny need to determine what numbers are prime and what numbers are composite for homework assignment. Cruz says that the number 5 is a composite number because it has the factors 2 and 2.5. Explain what is wrong with his reasoning
*August 5, 2010 by sai*

**Math**

Can you check my work and tell me if I did anything wrong? 1. With the functions: f(x) = x^2 + 3x and g(x) = -3 + x what is f(x) + g(x)? Answer: x^2 + 4x - 3 2. With the functions: f(x) = x + 4 and g(x) = x -3 what is (f*g)(x)? Answer: x^2 + x - 12 3. With the functions: f(x...
*January 26, 2015 by Jenny*

**Functions in Math**

Im looking at internet sites and Im not quite understanding functions. I have a question like; A function f(x) has the properties i) f(1) = 1 ii) f(2x) = 4f(x)+6 Could you help me out. I know nothing about functions.
*October 15, 2007 by Lena*

**Math**

There are 13 flavbors at a local ice cream parlor. Is the number 13 a prime number or a composite number? If it is composite, write the number as the product of prime numbers
*August 9, 2010 by Sai*

**math**

which of these statements about prime and composite numbers is true? F)all prime numbers are odd. G)all prime numbers have three factors. H)all composite numbers are divisible by two. J)all composite numbers have more then two factors i thinks it (J) but im not sure
*March 25, 2010 by george*

**Calculus**

We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic functions are any functions that can be made...
*September 13, 2007 by Kelly*

**Criminal Justice/Report Writing**

When a number of different witnesses provide descriptions of the suspect, it is considered: A. acceptable for speed and brevity to combine multiple descriptions into a composite description. B. good investigative tactics to combine multiple descriptions into a composite ...
*October 25, 2014 by Pat*

**math last one help**

sally drew a factor tree of a composite number and ended up with 4x4x5x5x3 as the prime factorization. explain what is wrong with this factorization 1. what is the correct prime factorization? 2. what is the composite number that was factored?
*August 29, 2013 by daniel*

**algebra 2**

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. B) using a composition of functions represent the situation in which the ...
*January 23, 2011 by carly*

**algebra 2**

can you answer this question? a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. B) using a composition of functions represent ...
*November 16, 2010 by rachel*

**calculus**

Suppose that f(x)= square root of x and g(x)= 3x-4 and you are asked to evaluvate the composite function f(g(0)). What is the complication that occurs in trying to find that composite function value? For waht values of x is it possible to evauvate f(g(x))? Please help me with ...
*February 3, 2011 by Pauline*

**Math (repost)**

Let f and g be defined by f(x) = 9-x such that 4<x<8 g(x) = x+2 such that 1<x<5 [the "<" signs are less than or equal to] Find the domains of both f o g and g o f algebraically. Find the range of f o g algebraically. I got the equation for f(g(x)), which is 7-x...
*September 5, 2009 by anonymous*

**Materials Science**

An isotropic epoxy resin (E=2GPa, ν=0.3) is reinforced by unidirectional glass fibers (Eglass=70GPa), aligned in the 2 direction, such that the fiber composite is transversely isotropic, with the 1-3 plane being the plane of isotropy. The elastic constants of the fiber ...
*October 1, 2014 by qwerty*

**Math**

Let f and g be defined by f(x) = 9-x such that 4<x<8 g(x) = x+2 such that 1<x<5 [the "<" signs are less than or equal to] Find the domains of both f o g and g o f algebraically. Find the range of f o g algebraically. I got the equation for f(g(x)), which is 7-x...
*September 5, 2009 by anonymous*

**Composite Functions**

I'm trying to make sure I got this question right. I'm supposed to find (g * f)(x) when f(x)x^2-2x and g(x)=√(x-15). This is what I've got: (g * f)(x) = g(f(x)) √ (x^2-2x)-15= √(x^2-2x-15)= √(x-5)(x+3)
*January 17, 2015 by Pax*

**advanced functions/precalculus**

1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)). 2. Give an example of two functions that satisfy the following conditions: - one has 2 zeros - one has ...
*January 15, 2014 by Diane*

**college algebra**

Let f(x) = square root (x + 2) and g(x) = x^2 − 2. Determine the domain of the composite function. (Enter your answer using interval notation.) f compose f ______? & Find the composite function. (f compose f)(x) = _____?
*October 21, 2013 by Dee*

**math**

Consider the given statements. 1. Every prime number is odd. 2. There are 8 prime numbers between 10 and 40. 3. There are 11 composite numbers between 0 and 20. 4. The number 4 is the smallest even composite number.
*July 15, 2014 by angela*

**algebra 2**

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. the answer is (1.06)(.7x) = .742x B) using a composition of functions ...
*January 22, 2011 by jennifer*

**algebra 2**

a store is offering a discount of 30% on a suit. There is a sales tax of 6%. A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied. the answer is (1.06)(.7x) = .742x B) using a composition of functions ...
*January 22, 2011 by jennifer*

**MATH**

We now have d dx [x5 + y8] = 5x4 + 8y7y' = d dx [9] = 0. Rearranging this, we get 8y7y' = ?????????? ------------------------------------- A table of values for f, g, f ', and g' is given. x f(x) g(x) f '(x) g'(x) 1 3 2 4 6 2 1 8 5 7 3 7 2 7 9 (a) If h(x) = f(g(x)), find h'(3...
*October 6, 2014 by Anonymous*

**Calculus**

Find the sum and difference functions f + g and f – g for the functions given. f(x) = 2x + 6 and g(x) = 2x - 6 f(x) = x^2 - x and g(x) = -3x + 1 f(x) = 3x^3 - 4 and g(x) = -x^2 + 3 State the domain and range for the sum and difference functions in #3. Find the product and the ...
*September 2, 2013 by Bee*

**math test**

Hi! I have a math test coming up tomorrow, and I need to prepare. but,i dont know how I should. . . any help would be great. she told us to: Be prepared to identify and explain functions, linear functions and proportional functions. Be prepared to use the new function notation...
*October 11, 2007 by Keon*

**Domain of composite function**

Can you please help me with the following questions? Find the domain of the composite function f * g. 12. f(x)=x+3, g(x)=1/(x+7) 15. f(x)=7x+70, g(x)=x+2
*September 14, 2007 by Soly*

**Math - Chain Rule**

I've been having some difficulities with this but I think I figured it out. Could you double check me and make sure I'm doing the correct steps? Differentiate and simplify the answer. f(x) = 2(3x+1)^4 (5x-3)^2 =2(3x+1)^4 [2(5x-3)(5)] + [8(3x+1)^3] (5x-3)^2 =2(3x+1)^4 [10(5x-3...
*August 25, 2006 by becky*

**math**

Consider the given statements. 1. Every prime number is odd. 2. There are 8 prime numbers between 10 and 40. 3. There are 11 composite numbers between 0 and 20. 4. The number 4 is the smallest even composite number. Which two given statements are incorrect? OptionsMark for ...
*July 15, 2014 by angela*

**Domain of composite function**

Find the domain of the composite function fog. f(x)=x^2+3;g(x)=sqrtx-4
*April 2, 2013 by Alley*

**Math**

use the functions f(x)=x+4 and g(x)=2x-5 to find the specified functions. (g X f)^-1 Would the answer be x+1 over 2?
*February 20, 2009 by Dan*

**college algebra**

Let f(x) = 1/x − 2 and g(x) = 1/x − 3 . Determine the domain of the composite function. (Enter your answer using interval notation.) g compose f _____? & Find the composite function. (g compose f)(x) = _____?
*October 21, 2013 by Dee*

**Composite Materials**

Can someone please help with this problem? A burnout test was performed to determine the volume fractions of constituents in a glass/epoxy composite. The following observations were made: Weight of empty crucible = 47.6504 g Weight of the crucible and small piece of composite...
*February 26, 2009 by Jim*

**Math - Functions**

For the real valued functions f(x) - |x| - 4 and g(x) = sqrt(5 - x) Find the composition of f o g and the domain in interval notation. Can someone help me solve this?
*May 2, 2007 by UnstoppableMuffin*

**Math - Functions**

Is it possible to graph linear functions like h(x) = 3x + 7 without doing a table of values? If it is, how? And I know the slope is 7, which means the y-intercept is (0,7).
*December 18, 2007 by Anonymous*

**Math**

Use the functions f(x)=x+4 and g(x)=2x-5 to find the specified functions. (g x f)^-1
*March 25, 2009 by Jake*

**Math**

Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United ...
*January 19, 2013 by Anonymous*

**modern physics - relativity**

A photon of energy E collides with a stationary particle of rest mass m0 and is absorbed by it . (A) what is the velocity of resulting composite particle ? (B) What is the mass of the resulting composite particle ? use conservasion of energy / momentum please show working
*June 7, 2011 by walter *

**special relativity **

A photon of energy E collides with a stationary particle of rest mass m0 and is absorbed by it. what is the velocity of the resulting composite particle ? what is the mass of the resulting composite particle? (use conservation of momentum and energy)
*June 7, 2011 by Deforest *

**math**

for the given functions f and g, find the specified value of the following functions and state their domains: f(x)=x-5; g(x)=2x^2 a.(f+g)(3)= b.(f/g)(3)= Can someone help me figure this out? pleeeease????
*March 27, 2013 by asia*

**math**

Tony and Tom are brothers.This year both of their ages are prime numbers. Last year both of their ages were composite numbers. Both of their ages will be composite numbers again over the next three years. If Tony and Tom are both teenagers, how old are they now?
*September 29, 2011 by peter*

**math**

Joel and jacob are brothers. This year both of their ages are prime numbers. Last year both of their ages were composite numbers.Both of their ages will be composite numbers again over the next three years. If joel and jacob are both teenagers, how old are they now?
*October 27, 2011 by peter*

**Algebra**

Use composition of functions to show that the functions f(x) = 5x + 7 and g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.
*July 29, 2009 by Alicia*

**math**

is 113 prime or composite
*July 1, 2009 by Anonymous*

**math**

is 39 a prime or a composite number?
*January 9, 2010 by makeeda*

**math**

WHAT are the frist 10 composite numbers
*January 12, 2011 by samantha*

**Math Grade 12 Advance Functions**

I need help understanding equivalent trigonometric functions! Can someone PLEASE help me because the test is tommorrow and the internet or my textbook isn't helping at all!
*December 19, 2012 by Buddy*

**math**

for the given functions f and g, find the specified value of the following functions and state the domain of each one. f(x)=2+3/x; g(x)=3/x a.(f-g)(2)= b.(f/g)(3)= how do I do this? I need help! it throws me off because of it being in fraction form.
*March 26, 2013 by marie*

**exponential functions in math**

my daughter needs some help studying for a unit test using exponential functions in math
*April 2, 2013 by tiffny*

**Math**

How to write a math story that includes 4 examples... Possible math topics include: introduction to functions investigating quadratics quadratics highs & lows exponential functions fiancial applications of exponential function acute triangle trigonometry I'm taken MCF3M math ...
*January 13, 2011 by Tarkan*

**Algebra**

Graph and label the following two functions: f(x)=(x^2+7x+12)/(x+4) g(x)=(-x^2+3x+9)/(x-1) 1. Describe the domain and range for each of these functions. 2. Determine the equation(s) of any asymptotes found in the graphs of these functions, showing all work. 3. Discuss the ...
*May 2, 2011 by Debra*

**6th grade MATH**

WHAT IS A COMPOSITE NUMBER AND WHY?
*August 18, 2010 by TEE*

**math**

is 2311 a prime or composite number?
*February 24, 2011 by Anonymous*

**Math**

Let f(x)= 2x^2, g(x)= 5x-6, and m(x)= 3x. Find and simplify the composite function g(m(f(x))).
*April 19, 2012 by Ariel*

**math**

Prime & composite numbers explain
*September 26, 2012 by jamie*

**Math**

What is the smallest positive composite integer?
*November 19, 2013 by John*

**Math **

How do you find the area if a composite shape?
*March 25, 2015 by Amy*

**Check my CALCULUS answers please! **

Any short explanation for things I got wrong would be great, too, if possible! Thanks in advanced! :) 8. Which of the following functions grows the fastest? ***b(t)=t^4-3t+9 f(t)=2^t-t^3 h(t)=5^t+t^5 c(t)=sqrt(t^2-5t) d(t)=(1.1)^t 9. Which of the following functions grows the ...
*October 7, 2013 by Samantha*

**math**

how do you figure out what prime and composite numbers are
*September 25, 2007 by sydnee*

**Math**

Let f = {(1,2), (2,3), (3,5), (4,7)} and g = {(1,4), (2,3), (3,1)} Express each composite as a set of ordered pairs. a) f of g
*January 15, 2008 by Alex*

**Math**

Let f = {(1,2), (2,3), (3,5), (4,7)} and g = {(1,4), (2,3), (3,1)} Express each composite as a set of ordered pairs. a) f of g
*January 15, 2008 by Alex*

**math**

how do i find the smallest composite number with 2,3,5,7,11 as factors
*October 1, 2008 by don*

**math**

Which of the given numbers are composite? 0, 1, 15, 19, 23, 31, 49, 55, 59, 87, 91, 97, 103, 105
*July 15, 2009 by scooby91320002*

**math 115**

what does composite and prime mean and reciprocal
*September 5, 2009 by p*