Answer
Please see the step by step proof below.
Work Step by Step
We prove the equation by substituting the function $f(x)=3^{x-1}$ to the left side of the expression:
$\frac{f(x+h)-f(x)}{h}=\frac{3^{x+h-1}-3^{x-1}}{h}=\frac{3^{x-1}3^h-3^{x-1}}{h}
=\frac{3^{x-1}(3^h-1)}{h}$
Thus we proved that $\frac{f(x+h)-f(x)}{h}=3^{x-1}(\frac{3^h-1}{h})$
