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

User Yussef
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1 Answer

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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.

User Arkadiusz K
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