Question

Let f(x)=3x-2. What is f^-1 (x) ?

Answer 1

Given the function:

f(x) = 3x - 2

Let's find the inverse of the function f⁻¹(x).

To find the inverse of the function, apply the following steps:

• Step 1.

Rewrite y for f(x)

`y=3x-2`

• Step 2.

Interchange the x and y variables:

`x=3y-2`

• Step 3.

Solve for y.

Add 2 to both sides:

`\begin{gathered} x+2=3y-2+2 \\ \\ x+2=3y \end{gathered}`

• Step 4.

Divide all terms by 3: