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 xintersepts? if any on the graph of f.
f. list the yinntercept, if any on the graph of f.
Please help me understand this, and show work please.
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1 answer

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.
xintersept = point where f ( x ) = 0
In this case 10 x ^ 2 = 0
Obviously x = 0 so
x inntercept point ( 0 , 0 )
f.
yinntercept = point where x = 0
In this case :
f ( x ) = 10 * 0 ^ 2 / ( 0 ^ 2 + 25 ) =
10 * 0 / ( 0 + 25 ) = 0 / 25 = 0
yinntercept 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 stepbystep 👍
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answered by Bosnian
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