SOLUTION: Need help on how to solve this: Given that h(x)=f(g(x)), find f(g) and g(x). f(g)doesn't equal g & g(x) doesn't equal x equations: h(x)=^3sqrt(x+2)-6 and h(x)=-4/x^2+x-1

Algebra ->  Equations -> SOLUTION: Need help on how to solve this: Given that h(x)=f(g(x)), find f(g) and g(x). f(g)doesn't equal g & g(x) doesn't equal x equations: h(x)=^3sqrt(x+2)-6 and h(x)=-4/x^2+x-1       Log On


   

Question 981380: Need help on how to solve this:
Given that h(x)=f(g(x)), find f(g) and g(x). f(g)doesn't equal g & g(x) doesn't equal x
equations: h(x)=^3sqrt(x+2)-6 and h(x)=-4/x^2+x-1

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
h(x)=3sqrt(x+2)-6

Try g%28x%29=x%2B2.
.
f%28x%29=sqrt%28x-6%29.
The intermediate step may be f%28g%28x%29%29=sqrt%28g%28x%29-6%29.

Resolving the composition on h%28x%29=-4%2Fx%5E2%2Bx-1 will not work the way you want. Maybe first convert to single rational expression?
%28-4%2Bx%5E2-x%29%2Fx%5E2
%28x%5E2-x-4%29%2Fx%5E2
Still would need to let x be assigned g(x).
Maybe another tutor would see how to find g and g for this one.