Friday

November 21, 2014

November 21, 2014

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

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 12:28pma.

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**

College algebra - Answer the questions about the following functions. f(x) = 14^...

Calculus - Find the point P on the graph of the function y=\sqrt{x} closest to ...

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 - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...

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 = ...

Calculus - Graph of a piecewised function is f(x)=1, x>0 and f(x)=-1, x<0 ...

Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...