Question

Which of the following equations represents the inverse of y = e2x - 9?

Answer 1

Answer:

y=1/2 (Inx+9)

Answer 2

Important:  write this function as y = e^(2x) - 9.  " ^ " indicates exponentiation.

To find the inverse function:

1) interchange x and y.  y becomes x and x becomes y:  x = e^(2y) - 9
2) solve this result for y:

             e^(2y) = x + 9                   Take the natural log of both sides:

              2y = ln(x+9) (domain is restricted to "x is greater than -9")

                            ln(x+9)
            Then y = -----------
                               2

This is the inverse function of y = e^(2x) - 9.