Question

What is the inverse of f(x)= 1/3x +2?

Answer 1

To determine the inverse of the function we need to follow these steps:

1 - Replace f(x) by y;

2 - Switch the places of x and y on the expression;

3 - Solve the expression for y;

4 - Replace y by f^-1(x).

Let's apply them to the given expression.

`\begin{gathered} y=(1)/(3)x+2 \\ x=(1)/(3)y+2 \\ (1)/(3)y=x-2 \\ y=3x-3\cdot2 \\ y=3x-6 \\ f^(-1)(x)=3x-6 \end{gathered}`

The inverse of the function is "3x - 6".