Answer:
[tex]g^{-1}(x)=1+10^{x/2}[/tex]
Step-by-step explanation:
Inverse Function
Let's call:
[tex]y=2 log(x-1)[/tex]
Divide by 2:
[tex]y/2=log(x-1)[/tex]
Assuming the base of the log is 10, apply exponential base 10:
[tex]10^{y/2}=x-1[/tex]
Solving for x:
[tex]x=1+10^{y/2}[/tex]
Swap variables:
[tex]y=1+10^{x/2}[/tex]
Calling this function the inverse:
[tex]\boxed{g^{-1}(x)=1+10^{x/2}}[/tex]
