### Instruction: Let $f(x)=7x+5$ and $g(x)=x-1$.  If $h(x)=f(g(x))$, then what is the inverse of $h(x)$?### Response: I need to find a function that undoes what $h(x)$ does to any input.
That means I have to reverse the order of applying $f$ and $g$, and also reverse what each function does.
So instead of first subtracting 1 and then multiplying by 7 and adding 5, I should first subtract 5 and then divide by 7 and then add 1.
That means the inverse of $h(x)$ is a function that does those operations, in that order, to any input.
I can write that function as $h^{-1}(x) = \frac{x-5}{7} + 1$.