# Precalculus

posted by .

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 input for a second function g(x). In this case, the composite is denoted g(f(x)) which is read "g composed with f of x" or "g of f of x."

**If you could help with anything I'd really appreciate it!! Thank you**

Suppose f and g are functions defined by the following table:
x) -3 -2 -1 0 1 2 3
f(x) 10 8 7 3 -4 -7 -8
g(x) 3 1 0 2 -3 -1 -2

i. Make a table of values for f(g(x)) with x= -3,-2,-1,0,1,2,3 Remember to always start with the innermost set of parentheses

ii. Make a table of values for g(g(x)) with x= -3,-2,-1,0,1,2,3.

iii. Explain why you cannot find the composite function g(f(x)).

a)Consider the two functions f(x)=-x^2+ 7 and g(x)=3x+4. Using input values of -1,2,0.5,and 8 for x:
1. Calculate f(g(x)) for each input value
2. Calculate g(f(x)) for each input value.

B) if f and g are two functions, what must be true about the domains and ranges of f and g in order for f(g(x)) to make sense? What must be true for g(f(x))to make sense?

• Precalculus -

If (f º g)(3) = 7, then f(x) and g(x) could be:
Select one:
a. f(x) = 3x2 – 10x + 4, g(x) = x + 2
b. f(x) = 2x – 3, g(x) = x2 – 4
c. f(x) = 3x + 1, g(x) = x – 3
d. f(x) = x2, g(x) = x – 2

## Similar Questions

1. ### Algebra Functions

I cannot for the life of me remember how to do this- Find the vertex of the graphs of the functions: Function #1: y=(x-4)(x+2) AND Function #2: y=2x^2-4x+1 Can someone help me get it PLz! OK - to find the vertex of these functions …
2. ### college algebra

find a real-life application of a quadratic function. State the application, give the equation of the quadratic function, and state what the x and y in the application represent. Choose at least two values of x to input into your function …
3. ### Math, Still Need Help!

Label each statement TRUE or FALSE. a. The sum of two one-to-one functions is one-to-one. b. The product of two one-to-one functions is one-to-one. c. If f is a one-to-one function and k is a real number (constant), then the function …
4. ### math

(a) In order to express the function y = 1010 x + 4, as a composition of two functions the outer of which is an exponential function, we would let u be equal to the inner function, u = , and then write y as a function of u, as follows: …
5. ### Calculus

In order to express the function y=12^19x+7 as a composition of two functions the outer of which is an exponential function,we would let u be equal to the inner function, u=19x+7, and then write y as a function of u, as follows: y= …
6. ### 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 …