Answer
$f^{-1}(x)=\frac{2x-9}{4}$
Work Step by Step
$f(x)=\frac{4x+9}{2} \longrightarrow y=\frac{4x+9}{2} \longrightarrow x=\frac{4y+9}{2} \longrightarrow y=\frac{2x-9}{4} \longrightarrow f^{-1}(x)=\frac{2x-9}{4}$
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