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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