Answer
$f^{-1}(x)=cos^{-1}(3-x) $,
range of $f(x)$: $[0, \pi]$ and $[2,4]$,
domain and range of $f^{-1}(x)$: $[2,4]$ and $[0, \pi]$
Work Step by Step
Step 1. $f(x)=-cos(x)+3 \longrightarrow y=-cos(x)+3 \longrightarrow x=-cos(y)+3 \longrightarrow y=cos^{-1}(3-x) \longrightarrow f^{-1}(x)=cos^{-1}(3-x) $
Step 2. We can find the domain and range of $f(x)$: $[0, \pi]$ and $[2,4]$
Step 3. We can find the domain and range of $f^{-1}(x)$: $[2,4]$ and $[0, \pi]$
