First slide

Functions (XII)

Question

The domain of $y = \cos^{- 1} \frac{1 - 2 x}{4}$ is

Moderate

A

$[- \frac{3}{2}, \frac{5}{2}]$
B

$[- 1, 1]$
C

$[0, 2]$
D

$[- \frac{1}{2}, \frac{3}{2}]$

Solution

The given function is defined if
$\begin{array}{l} - 1 \leq \frac{1 - 2 x}{4} \leq 1 i.e. if - 4 \leq 1 - 2 x \leq 4, \\ \Rightarrow - 5 \leq - 2 x \leq 3 \Rightarrow \frac{- 3}{2} \leq x \geq \frac{5}{2} \end{array}$

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