## College Algebra (10th Edition)

We know that if $a^x=y$, then $\log_a y=x$ and vice versa. Hence here if $y=f(x)$, then $a^y=x$. $a^y=(\frac{1}{a})^{-y}=x$, thus $-y=\log_{\frac{1}{a}}x=-f(x)$. Thus we proved what we had to.