AP EAMCET · Maths · Functions
The range of the function \(f(x)=x^2+\frac{1}{x^2+1}\) is
- A \([1, \infty)\)
- B \([2, \infty)\)
- C \(\left[\frac{3}{2}, \infty\right)\)
- D \((0,1]\)
Answer & Solution
Correct Answer
(A) \([1, \infty)\)
Step-by-step Solution
Detailed explanation
Given function \(f(x)=x^2+\frac{1}{x^2+1}=y\) (let) \[ \begin{aligned} & \Rightarrow \quad x^4+x^2+1=y\left(x^2+1\right) \text { and } y>0 \\ & \Rightarrow x^4+(1-y) x^2+(1-y)=0 \end{aligned} \] \(\because x \in \mathbf{R}\), so discriminant \(\geq 0\)…
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
- The period of
\(\left(\tan \theta-\frac{1}{3} \tan ^3 \theta\right)\left(\frac{1}{3}-\tan ^2 \theta\right)^{-1}\)
where \(\tan ^2 \theta \neq \frac{1}{3}\) isAP EAMCET 2010 Easy - Let be a straight line passing through the origin and be the straight line . If the intercepts made by the circle on and are equal, then which of the following equations representAP EAMCET 2021 Medium
- Find the equation of a circle with radius 5 units and touching the circle \(x^2+y^2-2 x-4 y-20=0\) at the point \((5,5)\).AP EAMCET 2020 Medium
- If \(\frac{3 x^2+x+1}{(x-1)^4}=\frac{a}{(x-1)}+\frac{b}{(x-1)^2}\) \(+\frac{c}{(x-1)^3}+\frac{d}{(x-1)^4}\)
then \(\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) is equal toAP EAMCET 2010 Medium - In any triangle , equalsAP EAMCET 2022 Medium
- The area (in sq. units) bounded by \(x=4, y=-4\) and \(y=x\) isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- The average translational kinetic energy of the oxygen molecules at a temperature of \(127^{\circ} \mathrm{C}\) is
\(\left(\right.\) Boltzmann constant \(\left.=1.38 \times 10^{-23} \mathrm{~J} \mathrm{~K}^{-1}\right)\)AP EAMCET 2025 Easy - A closed organ pipe of length ' \(L\) ' and an open organ pipe contain gases of densities \(\rho_1\) and \(\rho_2\) respectively. The compressibility of gases are equal in both the pipes. If the frequencies of their first overtones are same, then the length of the open organ pipe isAP EAMCET 2017 Medium
- Which of the following reactions does not involve liberation of oxygen?AP EAMCET 2016 Easy
- Two uniform stretched steel strings \(A\) and \(B\) are vibrating under the same tension. The first overtone of \(A\) is equal to the second overtone of \(B\). If the radius of \(A\) is twice that of \(B\), then the ratio of the lengths of the strings isAP EAMCET 2018 Medium
- Electromagnetic waves of energy flux \(75 \times 10^4\) \(\mathrm{Wm}^{-2}\) incidents normally on a surface of area \(40 \mathrm{~cm}^2\). If absorbs the surface the flux completely, the total momentum delivered to the surface in one second isAP EAMCET 2023 Easy
- \(0.1 \mathrm{~m}\) solution each of sodium sulphate, urea and sodium chloride are taken. The correct ratio of elevation of boiling point of these solutions isAP EAMCET 2018 Easy