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