The domain of the function $f(x)=\frac{1

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$.

Options:

(-∞, 0)

(-∞, ∞) - {0}

(-∞, ∞)

(0, ∞)

Correct Answer:

(-∞, 0)

Explanation:

$f(x)=\frac{1}{\sqrt{|x|-x}}$

For $x≥0,|x|-x=0$

⇒ f (x) is not defined for x ∈ [0, ∞]

$⇒ D_f=(-∞, 0)$