Question

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

Answer 1

`g^(-1)(x)=1+10^(x/2)`

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)}`