Question

GIven the function f(x) = 3x +1: (A) Find the inverse of f^-1(x). (B) Find f^-1(6). Show every step of your problem-solving.

Answer 1

`f(x)=3x+1\to y=3x+1\\\\\text{change x to y and y to x}\\\\x=3y+1\ \ \ \ \text{solve for y}\\\\3y+1=x\ \ \ \ |-1\\\\3y=x-1\ \ \ \ |:3\\\\y=(x-1)/(3)\\\\\boxed{f^(-1)(x)=(x-1)/(3)}\\\\f^(-1)(6)\to\text{put x=6 to the equation of the function}\ f^(-1)(x)\\\\f^(-1)(6)=(6-1)/(3)=(5)/(3)=1(2)/(3)\\\\\boxed{f^(-1)(x)=1(2)/(3)}`