Question

What equation represents the inverse of y = e^2x - 9?

Answer 1

The inverse of this function is y =
`(ln(x + 9))/(2)`

You can find the inverse of any function by switching the x and y values. Once you've done that, you can solve for the new y. The result will be the inverse of the function. The work for this one is below.

y =
`e^(2x) - 9` ----> Switch the x and y

x =
`e^(2y) - 9` -----> Add 9 to both sides

x + 9 =
`e^(2x)` ----> Take the natural log (ln) of both sides. This will case the e to cancel on the right side.

ln(x + 9) = 2y ----> Divide both sides by 2.

y =
`(ln(x + 9))/(2)`

This will be your inverse function.