Answer
$f^{-1}(x)=log_2(x-1)$
Work Step by Step
$f(x)=1+2^x \longrightarrow y=1+2^x \longrightarrow x=1+2^y \longrightarrow y=log_2(x-1) \longrightarrow f^{-1}(x)=log_2(x-1)$
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