Question

find the inverse function. f(x) = 3x - 1 f⁻¹(x) = (x + ?) / ?

Explanation:

Step1: Replace \( f(x) \) with \( y \)

\( y = 3x - 1 \)

Step2: Swap \( x \) and \( y \)

\( x = 3y - 1 \)

Step3: Solve for \( y \)

First, add 1 to both sides: \( x + 1 = 3y \)
Then, divide both sides by 3: \( y = \frac{x + 1}{3} \)
So the inverse function \( f^{-1}(x)=\frac{x + 1}{3} \)

Answer:

The numerator's box should be 1 and the denominator's box should be 3. So \( f^{-1}(x)=\frac{x + \boldsymbol{1}}{\boldsymbol{3}} \)