Answer
The inverse of the given function is $\color{blue}{f^{-1}(x) = 2x-1}$.
Work Step by Step
Replace $f(x)$ with $y$ to obtain $y=\frac{x+1}{2}$.
To find the inverse of this function, perform the following steps:
(1) Interchange $x$ and $y$ to obtain:
$x=\frac{y+1}{2}$
(2) Solve for $y$ to obtain:
$x=\frac{y+1}{2}
\\x(2)=y+1
\\2x=y+1
\\2x-1 =y$
(3) Replace $y$ with $f^{-1}(x)$ to obtain:
$f^{-1}(x) = 2x-1$
Therefore, the inverse of the given function is $\color{blue}{f^{-1}(x) = 2x-1}$.
