AP EAMCET · Maths · Functions
The domain of the function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), where \([x]\) denotes the greatest integer not more than \(x\), is
- A \((-\infty,-2) \cup(1,2)\)
- B \((-\infty,-2) \cup(-1,2)\)
- C \((-\infty,-2), \cup[-1,2]\)
- D \((-\infty,-1) \cup(1,2)\)
Answer & Solution
Correct Answer
(C) \((-\infty,-2), \cup[-1,2]\)
Step-by-step Solution
Detailed explanation
Given function \(f(x)=\sqrt{\frac{4-x^2}{[x]+2}}\), is define if \[ \frac{4-x^2}{[x]+2} \geq 0 \Rightarrow \frac{x^2-4}{[x]+2} \leq 0 \] So, either \(x^2-4 \leq 0\) From intervals Eqs. (iii) and (iv), \[ x \in(-\infty,-2) \cup[-1,2] \]
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
- The value of \(c\) such that the straight line joining the points \((0,3)\) and \((5,-2)\) is tangent to the curve \(y=\frac{c}{x+1}\) isAP EAMCET 2024 Easy
- If and , thenAP EAMCET 2021 Hard
- The line passing through the points \((1,1,-1)\) and \((3,-1,0)\) makes an angle of \(\operatorname{Tan}^{-1}\left(\frac{1}{\sqrt{8}}\right)\) with plane \(\sqrt{\lambda} x+3 y+6 z=17\). Then \(\lambda=\)AP EAMCET 2020 Easy
- The general solution of the differential equation isAP EAMCET 2020 Medium
- If \(\mathrm{A}\) and \(\mathrm{B}\) are symmetric matrices of same order such that \(\mathrm{AB}+\mathrm{BA}=\mathrm{X}\) and \(\mathrm{AB}-\mathrm{BA}=\mathrm{Y}\), then \((\mathrm{XY})^{\mathrm{T}}=\)AP EAMCET 2022 Medium
- \(\int e^x\left(\log x+\frac{1}{x^2}\right) d x=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- In a test a student either guesses or copies or knows the answer to answer a multiple choice question with four choices. The probability that he makes a guess is \(1 / 3\) and the probability that he copies the answer is \(1 / 6\). The probability that his answer is correct, given that he copied it is \(1 / 8\). The probability that he knew the answer to the question, given that he answered it correctly isAP EAMCET 2023 Hard
- If \(A\) and \(B\) are two independent events such that \(P(A)=0.3,
P(B)=x\) and \(P(A \cup B)=0.44\), then \(x=\)AP EAMCET 2022 Easy - The mole fraction of a solute in one molal ethanolic solution would beAP EAMCET 2021 Easy
- If \(C\) is the mid-point of line segment \(A B\) and \(P\) is any point not on the line \(A B\), thenAP EAMCET 2021 Hard
- \(\int_0^{\infty}\left(x^{12}+x^{-12}\right) \frac{\log x}{x} d x=\)AP EAMCET 2022 Hard
- If \(4^3+8^3+12^3+\ldots\) up to \(n\) terms \(=k n^2(n+1)^2\) (for all \(n \in \mathrm{N}\)), then \(k=\)AP EAMCET 2017 Hard