Relations and Functions · Class 12 · CBSE · Science Mathematics
Let f: R {−2} → R {1} be defined by f(x) = (x − 1)/(x + 2). If f is invertible, which is the correct expression for f⁻¹?
Practice question from Relations and Functions (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · MCQ · Q-276BC0
Let f: R \ {−2} → R \ {1} be defined by f(x) = (x − 1)/(x + 2). If f is invertible, which is the correct expression for f⁻¹?
- A.f⁻¹(x) = (1 − 2x)/(1 + x)
- B.f⁻¹(x) = (1 + 2x)/(1 − x)Correct answer
- C.f⁻¹(x) = (x + 1)/(2 − x)
- D.f⁻¹(x) = (2x − 1)/(x + 1)
Solution
Put y = (x − 1)/(x + 2). Then yx + 2y = x − 1, so x(y − 1) = −(1 + 2y), giving x = (1 + 2y)/(1 − y). Therefore, f⁻¹(x) = (1 + 2x)/(1 − x).
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