### Instruction: Let $f(x)=3x+4$ and $g(x)=2x-3$.  If $h(x)=f(g(x))$, then what is the inverse of $h(x)$?### Response: To find the inverse of $h(x)$, I need to first find $h(x)$ by plugging in $g(x)$ into $f(x)$.
That means $h(x)=f(2x-3)=3(2x-3)+4$.
To simplify, I can use the distributive property and combine like terms: $h(x)=6x-9+4=6x-5$.
Now I have $h(x)=6x-5$, and I want to find $h^{-1}(x)$, the inverse function.
To do that, I can switch the roles of $x$ and $y$, where $y=h(x)$, and then solve for $y$.
That is, I have $x=6y-5$, and I want to isolate $y$.
I can do that by adding $5$ to both sides and then dividing by $6$: $x+5=6y$, so $y=\frac{x+5}{6}$.
This means that $h^{-1}(x)=\frac{x+5}{6}$.