F(x) help show work

Question

Let f(x)=e^3x

 

(a.) Find the inverse function of f. Show work.

(b.) What is the domain of f ? What is the domain of the inverse function?

Answer 1

y = e^3x switch x and y for the inverse

x = e^3y solve for y, take natural logs of both sides

lnx = 3y

y = lnx/3 = f^-1(x) = the inverse function

domain of the inverse is x>0

range of f is y>0

domain of f = any real number

range of f^-1 = any real number