Question

What’s the inverse of the function?
f(x)=3^x+1

Answer 1

`y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= (\ln(x-1))/(\ln 3)\\\\\implies f^(-1)(x) = (\ln(x-1))/(\ln 3)`

Answer 2

The inverse of f(x)=3x+1 is f(x)−1=13x−13 .