TS EAMCET · Maths · Functions
\(f:[-2,2] \rightarrow[-2,2]\) and \(g:[-2,2] \rightarrow[0,4]\) are two functions defined as \(f(x)=\left\{\begin{array}{l}-2,-2 \leq x \leq 0 \ x^2-2,0 \leq x \leq 2\end{array}\right.\) and \(g(x)=|f(x)|+f(|x|)\), then
- A f and g are injective mappings
- B f and g are surjective mappings
- C f is bijective mapping and g is injective mapping
- D f is not bijective mapping and g is surjective mapping
Answer & Solution
Correct Answer
(B) f and g are surjective mappings
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\left\{\begin{array}{cc}-2, & -2 \leq x \leq 0 \\ x^2-2, & 0 \leq x \leq 2\end{array}\right.\)…
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
- Two sides of a square are along the lines \(x=-5\) and \(y=4\). The point of intersection of the diagonals is \((3,-4)\). The point of intersection of the tangents drawn to the circumcircle of the square at the two consecutive vertices lying on \(x=-5\) isTS EAMCET 2022 Hard
- If \(\sum_{n=1}^k \tan ^{-1}\left(\frac{1}{n^2+3 n+3}\right)=\tan ^{-1} \alpha\), then \(\alpha=\)TS EAMCET 2020 Medium
- \(x=\frac{1-\sqrt{y}}{1+\sqrt{y}} \Rightarrow \frac{d y}{d x}\) is equal toTS EAMCET 2009 Medium
- The angle of \(\triangle A B C\) are in an arithmetic progression. If the larger sides \(a, b\) satisfy the relation \(\frac{\sqrt{3}}{2} < \frac{b}{a} < 1\), then the possible values of the smallest side areTS EAMCET 2015 Easy
- A vector of length units is making an angle with each of the -axis and -axis. If another vector of length units is making an angle with each of the -axis and -axis, thenTS EAMCET 2019 Medium
- If \(\cos \mathrm{A}+\cos \mathrm{B}+\cos \mathrm{C}=0=\sin \mathrm{A}+\sin \mathrm{B}+\sin \mathrm{C}\), then \(\cos (\mathrm{A}-\mathrm{B})+\cos (\mathrm{B}-\mathrm{C})+\cos (\mathrm{C}-\mathrm{A})=\)TS EAMCET 2023 Easy
More PYQs from TS EAMCET
- Assertion (A) If \(A=15^{\circ}, B=17^{\circ}\) and \(C=13^{\circ}\), then \(\cot 2 A+\cot 2 B+\cot 2 C\) \(=\cot 2 A \cot 2 B \cot 2 C\) Reason (R) In a \(\triangle P Q R\), \(\tan \frac{P}{2} \tan \frac{Q}{2}+\tan \frac{Q}{2} \tan \frac{R}{2}+\tan \frac{P}{2} \tan \frac{R}{2}=1\) The correct option among the following isTS EAMCET 2020 Hard
- Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between block and table is 0.1 . Find the force \(F\), that must be given to the \(0.8 \mathrm{~kg}\) block such that it attains acceleration of \(5 \mathrm{~m} / \mathrm{s}^2\). (Assume, acceleration due to gravity, \(\left.g=10 \mathrm{~m} / \mathrm{s}^2.\right)\)
TS EAMCET 2019 Medium - The compressibility factor \(Z=\frac{p V}{n R T}\) for hydrogen gas a \(273 \mathrm{~K}\) and \(\mathrm{l}\) atm pressure isTS EAMCET 2020 Medium
- The equation of the pair of straight lines passing through the point \((2,3)\) and perpendicular to the pair of lines \(3 x^2-4 x y+5 y^2=0\) is \(a x^2+2 h x y+b y^2+2 g x+2 f y+c\) \(=0\) then \(a+b+c+f+g+h=\)TS EAMCET 2022 Easy
- A satellite is launched into a circular orbit of radius \(R\) around earth while a second satellite is launched into a orbit of radius \(1.02 R\). The percentage difference in the time periods of the two satellites is :TS EAMCET 2003 Easy
- A mental sphere of radius \(r\) and specific heat \(S\) is rotated about an axis passing through its centre at a speed of \(n\) rotations per second. It is suddenly stopped and \(50 \%\) of its energy is used in increasing its temperature. Then, the raise in temperature of the sphere isTS EAMCET 2002 Hard