Answer
$y=\frac{1}{4} \cdot 2^x$ or $y=2^{x-2}$
Work Step by Step
To find the inverse of the given function, perform the following steps:
(1) Interchange $x$ and $y$:
$$x=\log_2{4y}$$
(2) Write the equation in exponential form using the definition $y=\log_a{x} \longleftrightarrow a^y=x$:
$$2^x=4y$$
(3) Solve for $y$:
\begin{align*}
2^x&=4y\\\\
\frac{2^x}{4}&=y\\\\
y&=\frac{1}{4} \cdot 2^x\end{align*}
Note that $\dfrac{2^x}{4}=\frac{2^x}{2^2} = 2^{x-2}$.
Thus, the inverse of the given function is:
$y=\frac{1}{4} \cdot 2^x$ or $y=2^{x-2}$