GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 21

Question

The domain of the function $f$ defined by $f(x) = \frac{1}{\sqrt{x + |x|}}$ is.

• A. $\mathbb{R}$
• B. $\mathbb{R}^+$
• C. $\mathbb{R}- \{0\}$
• D. None of these

Answer 1

For positive $x,$ denominator is square root of a positive value and hence $f(x)$ is real. For negative $x,$ due to the absolute value operand, denominator becomes $0$  and $f(x)$ is infinity. So, correct answer for the domain of $f(x)$ here is the set of positive numbers.

Correct answer. B

Comments

is it technically a function as square root  of some number maps to 2 diff numbers one +ve and other -ve

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Its fine if the co-domain set is also positive.

Answer 2

Domain is Positive Real Numbers.

Hence correct answer is B.