Question

G(x) = 2 log(x - 1) what is the inverse

Answer 1

Answer:

$g^{-1}(x)=1+10^{x/2}$

Step-by-step explanation:

Inverse Function

Let's call:

$y=2 log(x-1)$

Divide by 2:

$y/2=log(x-1)$

Assuming the base of the log is 10, apply exponential base 10:

$10^{y/2}=x-1$

Solving for x:

$x=1+10^{y/2}$

Swap variables:

$y=1+10^{x/2}$

Calling this function the inverse:

$\boxed{g^{-1}(x)=1+10^{x/2}}$