Inverse functions

Question

If f(x)=3^x+1 then find f^-1(4)

Answer 1

For f(x) = 3^x + 1, a solution is (1, 4).

Therefore f^-1(4) = 1

Answer 2

Interchange y & x, then solve for this (new) y; it will be f^-1(x).

 

x = 3^y+1

 

x-1 = 3^y

 

ln(x-1) = y•ln3

 

f^-1(x) = ln(x-1)/ln3. 

 

So it looks as if f^-1(4) = 1.