If (g(x) = frac{x + 1}{x – 2}, x neq -2), find (g^{-1}(2)).
-
A.
3 -
B.
2 -
C.
(frac{3}{4}) -
D.
-3
Correct Answer: Option D
Explanation
(g(x) = frac{x + 1}{x + 2}, x neq 2)
Let y = x, then (g(y) = frac{y + 1}{y + 2})
Let x = g(y), so that (x = frac{y + 1}{y + 2})
(x(y + 2) = y + 1)
(xy + 2x = y + 1 implies xy – y = 1 – 2x)
(y(x – 1) = 1 – 2x implies y = frac{1 – 2x}{x – 1})
(y = g^{-1}(x) = frac{1 – 2x}{x – 1})
(g^{-1}(2) = frac{1 – 2(2)}{2 – 1} = -3)