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

##### 1 Answer

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

Hopefully this helps!