Answer
$f(-x)=a^{-x}=\left(\frac{1}{a}\right)^x=\frac{1}{a^x}=\frac{1}{f(x)}. $
Work Step by Step
We know that $a^{-x}=\left(\frac{1}{a}\right)^x=\frac{1}{a^x}.$
If $f(x)=a^x$, then substitute $-x$ in to obtain: $f(-x)=a^{-x}=\left(\frac{1}{a}\right)^x=\frac{1}{a^x}=\frac{1}{f(x)}. $
