The inverse of this function is y = [tex] \frac{ln(x + 9)}{2} [/tex]
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 = [tex] e^{2x} - 9 [/tex] ----> Switch the x and y
x = [tex] e^{2y} - 9 [/tex] -----> Add 9 to both sides
x + 9 = [tex] e^{2x} [/tex] ----> 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 = [tex] \frac{ln(x + 9)}{2} [/tex]
This will be your inverse function.
