Find the inverse of f(x) = (2x + 3)/(x - 1).

• A. (x+3)/(x-1)
• B. (x-2)/(x-1)
• C. (x+3)/(x-2)
• D. (x-3)/(x-2)

Answer: (C)

Finding the inverse means solving for the input in terms of the output and then swapping roles, so you get a function that undoes the original.

Start with y = (2x+3)/(x-1). Multiply both sides by (x-1): y(x-1) = 2x + 3. Expand: yx - y = 2x + 3. Move x terms to one side: yx - 2x = y + 3. Factor x: x(y - 2) = y + 3. Solve for x: x = (y + 3)/(y - 2). Therefore the inverse function is f^{-1}(x) = (x + 3)/(x - 2).

Domain notes: the original function is undefined at x = 1, so x ≠ 1 there. The inverse is undefined at x = 2, so x ≠ 2. This aligns with the original range not containing 2.