AP EAMCET · Maths · Functions
The domain of the function defined by
\(f(x)=\frac{-5}{4 x^2+1}+\sqrt{x^2-4}\) is
- A \(R\)
- B \((-\infty,-2)\)
- C \((-\infty,-2] \cup[2, \infty)\)
- D \((2, \infty)\)
Answer & Solution
Correct Answer
(C) \((-\infty,-2] \cup[2, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{-5}{4 x^2+1}+\sqrt{x^2-4}\) \(\because f(x)\) will be undefined if \(4 x^2+1=0\) or \(x^2-4 < 0\) \(\because 4 x^2+1 \neq 0\) for \(x \in R \quad\left\{x^2\right.\) is always positive \(\}\) Now, let \(x^2-4 < 0\)…
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 \(A\) is a non-zero square matrix of order \(n\) with \(\operatorname{det}(I+A) \neq 0\) and \(A^3=O\), where \(I, O\) are unit and null matrices of order \(n \times n\) respectively, then \((I+A)^{-1}\) is equal toAP EAMCET 2010 Hard
- Imaginary part of \(\frac{(1-i)^3}{(2-i)(3-2 i)}\) isAP EAMCET 2024 Easy
- I. Two non-zero, non-collinear vectors are linearly independent.
II. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?AP EAMCET 2005 Easy - Let and where denotes the greatest integer less than or equal to thenAP EAMCET 2020 Medium
- Let \(S\) be the set of all quadratic equations of the form \(x^2+b x+c=0\), where \(b, c \in\{1,2,3\), \(4,5,6\}\). If an equation is selected at random from \(S\), then the probability that the equation has real roots isAP EAMCET 2021 Medium
- \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-a x+b=0\). If \(\alpha^2+\beta^2\) and \(\alpha^3+\beta^3\) are the roots of the equation \(\mathrm{Ax}^2+\mathrm{Bx}+\mathrm{C}=0\), then \(\mathrm{C}=\)AP EAMCET 2023 Medium
More PYQs from AP EAMCET
- InAP EAMCET 2018 Medium
- A thin converging lens of focal length \(25 \mathrm{~cm}\) forms a sharp image of an object on a screen placed at a distance of \(75 \mathrm{~cm}\) from the lens. Later the screen is moved closer to the lens by a distance \(25 \mathrm{~cm}\). The distance through which the object is to be shifted so that its image on the screen is sharp again isAP EAMCET 2019 Hard
- The product of real of the equation \(|x|^{6 / 5}-26|x|^{3 / 5}-27=0\)AP EAMCET 2012 Medium
- If the vertex of a parabola is \((4,3)\) and its directrix is \(3 x+2 y-7=0\), then the equation of latus rectum of the parabola isAP EAMCET 2017 Easy
- If the variance of the distribution
\begin{array}{cccccccc}
\hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 8 & 11 & 17 & 20 & 24 & 32 \\
\hline \boldsymbol{f}_{\boldsymbol{i}} & 3 & 5 & 9 & 5 & 4 & 3 & 1
\end{array}
is 45.8 , then the variance of the distribution.
\begin{array}{llllllll}
\hline \boldsymbol{x}_{\boldsymbol{i}} & 10 & 18 & 24 & 36 & 42 & 50 & 66 \\
\hline \boldsymbol{f}_{\boldsymbol{i}} & 3 & 5 & 9 & 5 & 4 & 3 & 1 \\
\hline
\end{array}AP EAMCET 2018 Medium - Which one of the following is a secondary alcohol?AP EAMCET 2002 Easy