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: Option A
Explanation
(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})