First slide

Functions (XII)

Question

$If f : (- \infty, 2] ⟶ (- \infty, 4], where f (x) = x (4 - x), then f^{- 1} (x) is given by :$

Moderate

A

$2 - \sqrt{4 - x}$
B

$2 + \sqrt{4 - x}$
C

$- 2 + \sqrt{4 - x}$
D

$- 2 - \sqrt{4 - x}$

Solution

$\begin{array}{l} f (x) = 4 x - x^{2} = y \\ x^{2} - 4 x + y = 0 \\ f^{- 1} (x) = 2 - \sqrt{4 - x} \end{array}$

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