Let $f(x)=\frac{1}{[x]}+\sqrt{(2-x)x}$ a

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let $f(x)=\frac{1}{[x]}+\sqrt{(2-x)x}$ and [.] denotes the greatest integer, then the domain of f is

Options:

[0, 2]

[0, 1]

[1, 2]

(1, 2]

Correct Answer:

[1, 2]

Explanation:

For $D_f, f(x)$ must be real

$⇒ [x] ≠ 0$ and $(2 − x)x ≥ 0⇒ x ∉ [0, 1)$ and

$0 ≤ x ≤ 2 ⇒ x ∈ [1, 2] ⇒ D_f = [1, 2]$