Question

If \( f: \mathbb{R} \to \mathbb{R} \) such that \( f(x) = 3x - 4 \), then which of the following is \( f^{-1}(x) \)?

• A. \( \frac{1}{3}(x+4) \)
• B. \( \frac{1}{3}x - 4 \)
• C. \( 3x - 4 \)
• D. Undefined

Hint:

To find the inverse of a linear function, solve for \( x \) in terms of \( y \), then replace \( y \) with \( x \) to get \( f^{-1}(x) \).

Answer 1

The Correct Option is A

We are given the function \( f(x) = 3x - 4 \). To find the inverse \( f^{-1}(x) \), we will follow these steps: 1. Replace \( f(x) \) with \( y \): \[ y = 3x - 4 \] 2. Solve for \( x \) in terms of \( y \): \[ y + 4 = 3x \] \[ x = \frac{y+4}{3} \] 3. Now, replace \( y \) with \( x \) to get the inverse function: \[ f^{-1}(x) = \frac{x + 4}{3} \] Thus, the inverse function is \( f^{-1}(x) = \frac{1}{3}(x + 4) \).