Question

What is the inverse equation for h(x) = 2log(x-3) ?

Answer 1

Given the function:

$h(x)=2log\left(x-3\right)$

To find its inverse:

$\begin{gathered} y=2log\left(x-3\right) \\ x=2log\left(y-3\right) \end{gathered}$

solving for y:

$\frac{x}{2}=log(y-3)$$\begin{gathered} 10^{\frac{x}{2}}=y-3 \\ \\ 10^{\frac{x}{2}}+3=y \end{gathered}$

ANSWER

$h^^{-1}(x)=10^{\frac{x}{2}}+3$