Question

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

Answer 1

The inverse of this function is y = $\frac{ln(x + 9)}{2}$

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 = $\frac{ln(x + 9)}{2}$

This will be your inverse function.