Question

Which function below represents the inverse function of y = ln((x + 2)/3) + 1 ?

Answer 1

To find the inverse of the given function, isolate x from the equation:

`\begin{gathered} y=\ln ((x+2)/(3))+1 \\ \Rightarrow y-1=\ln ((x+2)/(3)) \\ \Rightarrow e^(y-1)=(x+2)/(3) \\ \Rightarrow3e^(y-1)=x+2 \\ \Rightarrow3e^(y-1)-2=x \\ \\ \therefore x=3e^(y-1)-2 \end{gathered}`

Swap x for y and y for x in the expression for x to find the inverse function:

`y=3e^(x-1)-2`

Therefore, the inverse function of y=ln((x+2)/3)+1 is y=3e^(x-1)-2.