TS EAMCET · Maths · Functions
Let \(f: \mathrm{A} \rightarrow \mathrm{B}\) be defined as \(f(x)=\frac{1}{2}-\tan \left(\frac{\pi x}{2}\right)\) and \(g: \mathrm{B} \rightarrow \mathrm{C}\) be defined \(g(x)=\sqrt{3+4 x-4 x^2}\). If A, B, C are subsets of \(\mathbb{R}\) and \(f\) is an onto function then the range of the function \(f(x)\) is
- A \((-\infty, \infty)\)
- B \([0, \infty)\)
- C \(\left[-\frac{1}{2}, \frac{3}{2}\right]\)
- D \([-1,1]\)
Answer & Solution
Correct Answer
(C) \(\left[-\frac{1}{2}, \frac{3}{2}\right]\)
Step-by-step Solution
Detailed explanation
Since \(f\) is an onto function Thus domain of \(\mathrm{g}(\mathrm{x})\) will be range of \(\mathrm{f}(\mathrm{x})\) Now, \(3+4 \mathrm{x}-4 \mathrm{x}^2 \geq 0\) to define \(\mathrm{g}(\mathrm{x})\) \[ \Rightarrow 4 \mathrm{x}^2-4 \mathrm{x}-3 \mathrm{x} 0 \] On solving we get…
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
- \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta\) is equal toTS EAMCET 2004 Medium
- The equation of the circle passing through the points of intersection of two circles and the point isTS EAMCET 2021 Easy
- The product of all the real roots of \(x^2-8 x+9-\frac{8}{x}+\frac{1}{x^2}=0\) isTS EAMCET 2017 Easy
- \(\mathrm{A}, \mathrm{B}\) are the events in a random experiment. If \(\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{1}{3}, \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4}\), then \(\mathrm{P}\left(\frac{\mathrm{A}^{\mathrm{c}}}{\mathrm{B}^{\mathrm{c}}}\right)+\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=\)TS EAMCET 2025 Medium
- Let \(\frac{1}{\left(x^2-3\right)^2}=\frac{A_1}{x-\sqrt{3}}+\frac{A_2}{(x-\sqrt{3})^2}\) \(+\frac{A_3}{x+\sqrt{3}}+\frac{A_4}{(x+\sqrt{3})^2}\). Then, consider the following statements (i) All the \(A_{\mathrm{i}}\) 's are not distinct (ii) There exists a pair, \(A_p\) and \(A_q\) such that \(A_p^2=A_q^2(p \neq q)\) (iii) \(\sum_{i=1}^4 A_i=\frac{1}{6}\) (iv) \(\sum_{i=1}^4 A_i=1\) Which one of the following is true?TS EAMCET 2019 Medium
- \(p\) points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points isTS EAMCET 2009 Hard
More PYQs from TS EAMCET
- Calculate enthalpy for formation of ethylene from the following data (I) \(\mathrm{C}_{\text {(graphite) }}+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g})\) \(\Delta H=393.5 \mathrm{~kJ}\) (II) \(\mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l)\); \(\Delta U=-256.2 \mathrm{~kJ}\) (III) \(\begin{array}{r}\mathrm{C}_2 \mathrm{H}_4(g)+3 \mathrm{O}_2(g) \rightarrow 2 \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) ; \ \Delta H=-1410.8 \mathrm{~kJ}\end{array}\)TS EAMCET 2007 Easy
- \(y-x=0\) is the equation of a side of a triangle ABC. The orthocentre and circumcentre of the triangle ABC are respectively \((5,8)\) and \((2,3)\). The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle isTS EAMCET 2025 Hard
- The number of common tangents to the two circles \(x^2+y^2-8 x+2 y=0 \quad\) and \(x^2+y^2-2 x-16 y+25=0\) is :TS EAMCET 2006 Medium
- A hollow cylinder and a solid cylinder initially at rest at the top of an inclined plane are rolling down without slipping. If the time taken by the hollow cylinder to reach the bottom of the inclined plane is 2 s , the time taken by the solid cylinder to reach the bottom of the inclined plane isTS EAMCET 2024 Medium
- If \(0 \leq x < \frac{3}{4}\) then the number of values of \(x\) satisfying the equation \(\operatorname{Tan}^{-1}(2 x-1)+\operatorname{Tan}^{-1} 2 x=\operatorname{Tan}^{-1} 4 x-\operatorname{Tan}^{-1}(2 x+1)\) isTS EAMCET 2025 Medium
- If \(\frac{x^2+5}{\left(x^2+1\right)(x-2)}=\frac{A}{x-2}+\frac{B x+C}{x^2+1}\), then \(A+B+C=\)TS EAMCET 2017 Easy