If (f(x) = frac{1}{2 – x}, x neq 2), find (f^{-1}(-frac{1}{2})).
-
A.
4 -
B.
0 -
C.
-2 -
D.
-4
Correct Answer: Option A
Explanation
(f(x) = frac{1}{2 – x}, x neq 2)
(f(y) = frac{1}{2 – y})
(x = frac{1}{2 – y}) (Let x = f(y))
(2x – xy = 1 implies y = frac{2x – 1}{x})
(therefore f^{-1}(x) = frac{2x – 1}{x})
(f^{-1}(-frac{1}{2}) = frac{2(-frac{1}{2}) – 1}{-frac{1}{2}})
= (-2 times -2 = 4)