Given that (f : x to frac{2x – 1}{x + 2}, x neq -2), find (f^{-1}), the inverse of f.
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A.
(f^{-1} : x to frac{1+2x}{2-x}, x neq 2) -
B.
(f^{-1} : x to frac{1-2x}{x+2}, x neq -2) -
C.
(f^{-1} : x to frac{1-2x}{x-2}, x neq 2) -
D.
(f^{-1} : x to frac{1+2x}{x+2}, x neq -2)
Correct Answer: Option A
Explanation
(f(x) = frac{2x – 1}{x + 2})
(y = frac{2x – 1}{x + 2})
(x = frac{2y – 1}{y + 2} implies x(y + 2) = 2y – 1)
(xy – 2y = -1 – 2x implies y = frac{-1 – 2x}{x – 2})
(f^{-1} : x to frac{1 + 2x}{2 – x} ; x neq 2)