SOLUTION: find f and g such that h=f*g where h(x)=(1/2x-3)^3 and the inner function g is rational

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Question 114785: find f and g such that h=f*g where h(x)=(1/2x-3)^3 and the inner function g is rational
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is this a function composition, or just multiplication? If it's a composition, then...


If h%28x%29=%281%2F%282x-3%29%29%5E3 and h(x)=f(g(x)), then simply let g%28x%29=1%2F%282x-3%29 and f%28x%29=x%5E3.

Notice if we evaluate f(g(x)), then we get

f%28g%28x%29%29=%28g%28x%29%29%5E3=%281%2F%282x-3%29%29%5E3

So this shows that if g%28x%29=1%2F%282x-3%29 and f%28x%29=x%5E3, then h%28x%29=%281%2F%282x-3%29%29%5E3