Question

Multiple Choice Which of the following is the inverse of \(f(x)=3 x-2 ? \mathrm{}\)

Short answer

The inverse of the function \( f(x)=3x-2 \) is \( f^{-1}(x) = (x + 2) / 3 \).

Step-by-step solution

Replace function notation

Firstly, replace \( f(x) \) with \( y \). So, the equation becomes: \( y = 3x - 2 \)

Interchange x and y

Next, interchange \( x \) and \( y \). This yields: \( x = 3y - 2 \)

Solve the equation for y

Lastly, solve the equation for \( y \), our new \( f(x) \) after interchanging. Add 2 to both sides of the equation to get: \( x + 2 = 3y \). Then divide each side by 3 to get: \( y = (x + 2) / 3 \)

Convert back to function notation

After finding the value of \( y \), convert back to function notation. So, the inverse function, \( f^{-1}(x) \), is: \( f^{-1}(x) = (x + 2) / 3 \)