A function f is defined on R, the set of real numbers, by: \(f : x \to \frac{x + 3}{x - 2}, x \neq 2\), find \(f^{-1}\).

A.

\(f^{-1} : x \to \frac{2x + 3}{x - 1}, x \neq 1\)

B.

\(f^{-1} : x \to \frac{x + 3}{x + 2}, x \neq -2\)

C.

\(f^{-1} : x \to \frac{x - 1}{2x + 3}, x \neq -\frac{3}{2}\)

D.

\(f^{-1}: x \to \frac{x - 2}{x + 3}, x \neq -3\)

Correct answer is A

\(f(x) = \frac{x + 3}{x - 2}\) 

\(f(y) = \frac{y + 3}{y - 2}\)

Let f(y) = x,

\(x = \frac{y + 3}{y - 2}\)

\(x(y - 2) = y + 3\)

\(xy - y = 2x + 3 \implies y(x - 1) = 2x + 3\)

\(y = \frac{2x + 3}{x - 1}\)