inverse function

Question

find the inverse for each of the following functions f(x)=ln(2+4x)

Answer 1

Let y=f(x)=ln(2+4x).

e^y=2+4x,

4x=e^y-2,

x=¼(e^y-2).

Let g(y)=¼(e^y-2), then g(x)=¼(e^x-2) because the variable is only a placeholder in the function.

But g(x) is the inverse of f(x), that is, g(x)=f^-1(x), so f^-1(x)=¼(e^x-2).