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