### 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: To find the inverse of a function, I need to switch the roles of x and y and solve for y.
So I'll start by writing y = h(x) and then replace h(x) with f(g(x)).
That gives me y = f(g(x)) = f(x-1) = 7(x-1) + 5 = 7x - 2.
Now I'll switch x and y and get x = 7y - 2.
To solve for y, I'll add 2 to both sides and then divide by 7.
That gives me y = (x + 2)/7.
This is the inverse of h(x), so I'll write it as h^-1(x) = (x + 2)/7.