Homework Help: calculus

Posted by Help--Please help!!!! on Sunday, December 16, 2012 at 9:48am.

answer the questions about the following function
f(x)= 10x^2/x^4+25

a. is the point (-sqrt 5,1) on the graph
b. if x=3, what is f(x)? what point is on the graph of f?
c. if f(x)=1, what is x? what points are on the graph?
d. what is the domain of f?
e. list the x-intersepts? if any on the graph of f.
f. list the y-inntercept, if any on the graph of f.

Please help me understand this, and show work please.

calculus - Bosnian, Sunday, December 16, 2012 at 12:28pm
a.

When x = sqrt ( 5 )

f ( x ) = 10 x ^ 2 / ( x ^ 4 + 25 ) =

10 * sqrt ( 5 ) ^ 2 / ( sqrt ( 5 ) ^ 4 + 25 ) =

10 * 5 / ( 25 + 25 ) = 50 / 50 = 1

yes

b.

When x = 3

f ( x ) = 10 x ^ 2 / ( x ^ 4 + 25 ) =

10 x ^ 2 / ( x ^ 4 + 25 ) =

10 * 3 ^ 2 ( 3 ^ 4 + 25 ) =

10 * 9 / ( 81 + 25 ) =

90 / 106 = 2 * 45 / ( 2 * 53 ) = 45 / 53

c.

10 x ^ 2 / ( x ^ 4 + 25 ) = 1 Multiply both sides by ( x ^ 4 + 25 )

10 x ^ 2 = x ^ 4 + 25

Substitution:

x ^ 2 = z

x ^ 4 = z ^ 2

10 z = z ^ 2 + 25

Exact solutions are :

z = + OR - 5

x ^ 2 = z

x = + OR - sqrt ( 5 )

d.

x ^ 4 + 25 differently of = 0

x ^ 4 are olway positive and

x ^ 4 + 25 are olvay positive so Domain = all real numbers

e.

x-intersept = point where f ( x ) = 0

In this case 10 x ^ 2 = 0

Obviously x = 0 so

x -inntercept point ( 0 , 0 )

f.

y-inntercept = point where x = 0

In this case :

f ( x ) = 10 * 0 ^ 2 / ( 0 ^ 2 + 25 ) =

10 * 0 / ( 0 + 25 ) = 0 / 25 = 0

y-inntercept point also ( 0 , 0 )

P.S:

If don't know how to solve equation:

10 z = z ^ 2 + 25

In google type:
quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type:

10 z = z ^ 2 + 25

and click option solve it

You will see solution step-by-step

Answer this Question

Related Questions

Algebra - Below is the graph of a polynomial function f with real coefficients. ...
college algebra, Please help!! - Answer the following function. f(x)=2x^2-x-1 A...
college algebra, Please help!! - Answer the following function. f(x)=2x^2-x-1 A...
calculus - Find the equation of the line tangent to the graph of the given ...
Calculus - There is a point (P) on the graph of [x^2+y^2- 136 x + 12 y + 4560 = ...
Calculus - There is a point (P) on the graph of [x^2+y^2- 136 x + 12 y + 4560 = ...
Math: Calculus - Answer the following questions for the function f(x) = \frac{ x...
Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...
Math - I solved the equation below and got an answer of 9+-sqrt(57) but i don;t ...
Calculus - Find dy/dx of the function 10x^2+4y^2=sqrt(7). Is the answer 20x+8y=0...

For Further Reading

First Name:
School Subject:
Answer: