Find the domain of $f(x)=\sqrt{\cos(\sin

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Find the domain of $f(x)=\sqrt{\cos(\sin x)}$.

Options:

$x ∈ R$

$x ∈ I$

$x ∈ N$

Cannot be determined

Correct Answer:

$x ∈ R$

Explanation:

$f(x)=\sqrt{\cos(\sin x)}$ is defined if

$\cos(\sin x)≥0$

As we know, $-1 ≤ \sin x ≤ 1$ for all x.

So, $\cos θ≥0$

(Here, $θ= \sin x$ lies in the first and fourth quadrants)

i.e., $\cos (\sin x) ≥ 0$ for all x

i.e., $x ∈ R$

Thus, the domain f(x) is R.