First slide

Functions (XII)

Question

$The domain of f (x) = \sqrt{\cos (\sin x)}$ is

Moderate

A

$R$
B

$R^{+}$
C

$R^{-}$
D

$ϕ$

Solution

$f (x) = \sqrt{\cos (\sin x)} is defined if$ $\cos (\sin x) \geq 0 - - - - (1)$
$As we know, - 1 \leq \sin x \leq 1 for all x \in R . So,$ $\cos θ \geq 0$
$(Here, θ = \sin x lies in the first and fourth quadrants)$
$i.e., \cos (\sin x) \geq 0 for all x$
$i.e., x \in R$
$Thus, the domain of f (x) is R .$

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