To determine the inverse of the given function , change f(x) to y, switch x and y and solve for x.
[tex] \\
\
f(x)=e^{2x}-4\\
\\
y=e^{2x}-4\\
\\
\Rightarrow e^{2y}=x+4\\
\\
\
\Rightarrow lne^{2y}=ln(x+4)\\
\\
\
\Rightarrow 2y=ln(x+4)\\
\\
\Rightarrow y=\frac{ln(x+4)}{2}\\
\\
\Rightarrow f^{-1}(x)=\frac{ln(x+4)}{2}\\ [/tex]
