If $y=\frac{\sqrt{x^2-4}}{\cos ^{-1}(2-x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $y=\frac{\sqrt{x^2-4}}{\cos ^{-1}(2-x)}$ , then the domain of y is :

Options:

[–2, 3]

[1, 2]

[2, 3]

[–2, 2]

Correct Answer:

[2, 3]

Explanation:

We know that

$x^2- 4 ≥ 0$ and $– 1 ≤ 2 – x < 1$

$x^2- 4 ≥ 0$

$⇒x^2≥4$

$|x|≥2$

$x≥2$

$x≤-2$

$– 1 ≤ 2 – x < 1$

so $1 ≤ x ≤3$

⇒ intersection of both of them gives

$2 ≤ x ≤3⇒x∈[2,3]$ domain