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**TaylorM0192** #1.)

Given $\displaystyle f(x) = x+3$ and $\displaystyle h(x) = 4x-4 <=> 4(x-1)$; find a function $\displaystyle g(x)$ such that $\displaystyle g(f(x)) = h(x) <=> g(x+3) = 4(x-1)$.

I'm having trouble determining what $\displaystyle g(x)$ should be - I don't know the method to determine this. If I was just asked to find any two functions whos composition resulted in $\displaystyle h(x$) I would have just decomposed $\displaystyle h(x)$ as $\displaystyle a(x) = 4x$ and $\displaystyle b(x) = x-1 <=> a(b(x)) = 4(x-1)$ - but I'm obviously forced to use the inside function $\displaystyle f(x) = x+3$.