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What is the inverse of the function f(x) = 2x - 3

A. f ^ - 1 * (x) = - 2x + 3

B. f ^ - 1 * (x) = 1/(2x - 3)

C. f ^ - 1 * (x) = (x + 3)/2

D. f ^ - 1 * (x) does not exist

1 answer

To find the inverse of the function \( f(x) = 2x - 3 \), we follow these steps:

  1. Replace \( f(x) \) with \( y \): \[ y = 2x - 3 \]

  2. Swap \( x \) and \( y \): \[ x = 2y - 3 \]

  3. Solve for \( y \): \[ x + 3 = 2y \] \[ y = \frac{x + 3}{2} \]

Now, we replace \( y \) with \( f^{-1}(x) \): \[ f^{-1}(x) = \frac{x + 3}{2} \]

Thus, the correct answer is: C. \( f^{-1}(x) = \frac{x + 3}{2} \)