How do I find the inverse function of f(x)=e^(3x)-4 ? And what is it's range ?

1 Answer
Noah G
Apr 16, 2018

To find the inverse algebraically, switch the x and ys.

x = e^(3y) -4

x +4 = e^(3y)

ln(x+ 4) = ln(e^(3y))

ln(x + 4) = 3y

y = f^-1(x) = 1/3ln(x +4)

Since the inverse of the function is the original function reflected over the line y =x, the domain of the original function becomes the range of the inverse and vice versa. Since y = e^(3x) -4 has a domain of all the real numbers, y = 1/3ln(x+ 4) will have a range of all the real numbers.

Hopefully this helps!

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