Let f(x) = (x − 1)/(x + 2), x ≠ −2. The inverse function f⁻¹(x) is: A. (2x + 1)/(1 − x) B. (2x − 1)/(x + 1) C. (x + 2)/(x − 1) D. (1 − 2x)/(x − 1) Answer: A) (2x + 1)/(1 − x) Explanation: y = (x−1)/(x+2) → y(x+2) = x−1 → yx + 2y = x − 1 → yx − x = −2y − 1 → x(y−1) = −(2y+1) → x = (2y+1)/(1−y). So f⁻¹(x) = (2x+1)/(1−x).

imo class 12 relations and functions

Let f(x) = (x − 1)/(x + 2), x ≠ −2. The inverse function f⁻¹(x) is:

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Let f(x) = (x − 1)/(x + 2), x ≠ −2. The inverse function f⁻¹(x) is:

Answer: A) (2x + 1)/(1 − x)

Explanation: y = (x−1)/(x+2) → y(x+2) = x−1 → yx + 2y = x − 1 → yx − x = −2y − 1 → x(y−1) = −(2y+1) → x = (2y+1)/(1−y). So f⁻¹(x) = (2x+1)/(1−x).