1. The problem asks to find the inverse of the function \(h(x)=\frac{3}{4}x+12\). 2. To find the inverse function \(h^{-1}(x)\), we start by replacing \(h(x)\) with \(y\): \[y=\frac{3}{4}x+12\] 3. Next, we swap \(x\) and \(y\) to find the inverse: \[x=\frac{3}{4}y+12\] 4. Now, solve for \(y\): \[x-12=\frac{3}{4}y\] 5. Multiply both sides by \(\cancel{\frac{4}{3}}\) to isolate \(y\): \[\cancel{\frac{4}{3}}(x-12)=\cancel{\frac{4}{3}}\frac{3}{4}y\] \[y=\frac{4}{3}(x-12)\] 6. Therefore, the inverse function is: \[h^{-1}(x)=\frac{4}{3}(x-12)\] 7. This means to find the input \(x\) for the original function given an output, we use \(h^{-1}(x)\).