Question

Find the inverse of the following function:

f(x)=2^(x-1)+3

Answer 1

ln(y/6)+1=x

Answer 2

ln both sides, then solve for x

Answer 3

\[f(x)=2^{x-1}+3\]\[f(x)-3=2^{x-1}\]\[\log_2{(f(x)-3)}=x-1\]\[1+\log_2{(f(x)-3)}=x\]\[\log_2{(2f(x)-6)}=x\]\[\Rightarrow\quad f^{-1}(x)=\log_2{(2x-6)}\]