How to find the inverse of this exponential function?

Question

Here is the function... It is $y=e^{x-3}+5$, I have no clue how to find the inverse of it. I graphed the function but now it says find the inverse and graph it. I do not know how to graph it.

Answer 1

$$y=e^{x-3}+5\iff e^{x-3}=y-5\iff x-3=\log(y-5)\iff x=\log(y-5)+3$$

thus the inverse is $\,g(x)=\log(x-5)+3\,$

Answer 2

Hint: Solve the equation $y = e^{x-3} + 5$ for $x$.

Answer 3

To draw the inverse

(1) Draw the original curve.

(2) Draw the line $y=x$.

(3) Reflect the original curve in the double-sided mirror $y=x$.