AP EAMCET · Maths · Functions
If \(x\) is real, then the range of \(\frac{x^2+2 x+1}{x^2+2 x+7}\) is
- A \([0,1)\)
- B \((-\infty, 0) \cup(1, \infty)\)
- C \((0,1)\)
- D \(R\)
Answer & Solution
Correct Answer
(A) \([0,1)\)
Step-by-step Solution
Detailed explanation
\begin{array}{lc} \text {} & \text { Let } \frac{x^2+2 x+1}{x^2+2 x+7}=y, \\ \because & y \neq 1 \\ \Rightarrow & (y-1) x^2+2(y-1) x+(7 y-1)=0 \\ \because & x \in R \\ \text { so, } & D \geq 0 \\ \Rightarrow & 4(y-1)^2-4(y-1)(7 y-1) \geq 0 \\ \Rightarrow & (y-1)[y-1-7 y+1] \geq…
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
- A circle touches the line \(2 x+y-10=0\) at \((3,4)\) and passes through the point \((1,-2)\). Then a point that lies on the circle isAP EAMCET 2025 Medium
- The equation of the circle concentric with the circle \(x^2+y^2-6 x+12 y+15=0\) and of double its area isAP EAMCET 2010 Hard
- If and , thenAP EAMCET 2021 Hard
- \(P\) is a point on \(x+y+5=0\), whose perpendicular distance from \(2 x+3 y+3=0\) is \(\sqrt{13}\), then the coordinates of \(P\) are:AP EAMCET 2024 Easy
- The general solution of the equation \(\sin ^2 \theta+3 \cos ^2 \theta=5 \sin \theta\) isAP EAMCET 2024 Easy
- If \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) and \(\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}\) are defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3-\mathrm{x}\) and \(g(x)=\sin 2 x\), then the value of \(x \in(0,2 \pi)\) that satisfy \(\mathrm{f}(\mathrm{g}(\mathrm{x}))>0\), lie in the intervalAP EAMCET 2023 Medium
More PYQs from AP EAMCET
- An object is fixed at the bottom of a vessel and water is filled in the vessel upto a height of \(10 \mathrm{~cm}\). A plane mirror is placed at a height of \(7 \mathrm{~cm}\) from the surface of water in such a way that its reflecting surface faces the water. The distance of the image from the mirror is (Refractive index of water, \(n=1.33\) )AP EAMCET 2019 Hard
- A Young double slit experimental setup is immersed in water of refractive index It has slit separation and the distance between slits and screen is . If the wavelength of incident light on slits is then the fringe width on screen isAP EAMCET 2019 Medium
- A small block of mass \(20 \mathrm{~g}\) and charge \(4 \mathrm{mC}\) is released on a long smooth inclined plane of inclination angle of \(45^{\circ}\), A uniform horizontal magnetic field of \(1 \mathrm{~T}\) is acting parallel to the surface, as shown in the figure. The time from the start when the block loses contact with the surface of the plane is
AP EAMCET 2019 Hard - The line \(y=6 x+1\) touches the parabola \(y^2=24 x\). The coordinates of a point \(P\) on this line, from which the tangent to \(y^2=24 x\) is perpendicular to the line \(y=6 x+1\), isAP EAMCET 2018 Easy
- In the following reaction, \(A\) and \(B\) respectively are
\(A \stackrel{\mathrm{HBr}}{\longrightarrow} \mathrm{C}_2 \mathrm{H}_5 \mathrm{Br} \stackrel{B}{\longrightarrow} A\)AP EAMCET 2002 Easy - A mercury drop of radius 1 cm is divided into \(10^6\) droplets of equal size. If surface tension of mercury is \(35 \times 10^{-3} \mathrm{Nm}^{-1}\), then the change in suface energy in the process isAP EAMCET 2025 Medium