MHT CET · Maths · Functions
The domain of the function \(f(x)=\frac{1}{\sqrt{x+|x|}}\) is
- A \((-\infty, 0)\)
- B \((2,5)\)
- C \((0, \infty)\)
- D \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(C) \((0, \infty)\)
Step-by-step Solution
Detailed explanation
\(
f(x)=\frac{1}{\sqrt{x+|x|}}
\)
Here \(x+|x| \geq 0\) and \(\sqrt{x+|x|} \neq 0\)
\(
\therefore \mathrm{x}+|\mathrm{x}|>0
\)
Now when \(x>0, x+|x|=x+x \Rightarrow 2 x>0\).
When \(\mathrm{x} < 0, \mathrm{x}+|\mathrm{x}|=\mathrm{x}-\mathrm{x}=0\)
\(\therefore \mathrm{x}>0\) is the required domain.
f(x)=\frac{1}{\sqrt{x+|x|}}
\)
Here \(x+|x| \geq 0\) and \(\sqrt{x+|x|} \neq 0\)
\(
\therefore \mathrm{x}+|\mathrm{x}|>0
\)
Now when \(x>0, x+|x|=x+x \Rightarrow 2 x>0\).
When \(\mathrm{x} < 0, \mathrm{x}+|\mathrm{x}|=\mathrm{x}-\mathrm{x}=0\)
\(\therefore \mathrm{x}>0\) is the required domain.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the line passing through the points \((a, 1,6)\) and \((3,4, b)\) crosses the yz-plane at the point \(\left(0, \frac{17}{2}, \frac{-13}{2}\right)\), thenMHT CET 2022 Medium
- The area of the region bounded by the curve \(y=4 x-x^{2}\) and the \(x\) -axis isMHT CET 2020 Easy
- The differential equation \(y^{\prime}=\frac{y}{x+\sqrt{x y}}\) has general solution given by (Where \(C\) is a constant of integration.)MHT CET 2022 Medium
- A fair die with numbers 1 to 6 on their faces is thrown. Let \(\mathrm{X}\) denote the number of factors of the number, on the uppermost face, then the probability distribution of \(\mathrm{X}\) isMHT CET 2023 Easy
- \(\operatorname{Cos}^2 48^{\circ}-\sin ^2 12^{\circ}=\)
,if \(\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}\)MHT CET 2022 Easy - The value of \(\int \frac{\mathrm{d} x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}\) is equal toMHT CET 2024 Medium
More PYQs from MHT CET
- A straight line L through the point \((3,-2)\) is inclined at an angle of \(60^{\circ}\) to the line \(\sqrt{3} x+y=1\). If L also intersects the X -axis, then the equation of \(L\) isMHT CET 2024 Medium
- If \(x=f(t)\) and \(y=g(t)\), then the value of \(\frac{d^{2} y}{d x^{2}}\) isMHT CET 2010 Easy
- \(\lim _{n \rightarrow \infty}\left[\frac{1}{1-\mathrm{n}^4}+\frac{8}{1-\mathrm{n}^4}+\ldots \ldots \ldots \ldots . .+\frac{\mathrm{n}^3}{1-\mathrm{n}^4}\right]=\)MHT CET 2025 Medium
- In melde's experiment, when the tension decreases by \(0.009\) kg-wt, the number of
loops changes from 4 to \(5 .\) The initial tension isMHT CET 2020 Medium - Following is the probability distribution of smart phones sold in a shop per day
Then \(E(x)=\)MHT CET 2022 Easy - The ratio of energy required to raise a satellite to a height ' \(h\) ' above the earth's surface to that required to put it into the orbit at the same height is ( \(\mathrm{R}=\) radius of earth)MHT CET 2023 Medium