WBJEE · Maths · Functions
If the function \(f: R \rightarrow R\) is defined by \(f(x)=\left(x^{2}+1\right)^{35}, \forall x \in R,\) then \(f\) is
- A one-one but not onto
- B onto but not one-one
- C neither one-one nor onto
- D both one-one and onto
Answer & Solution
Correct Answer
(C) neither one-one nor onto
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\left(x^{2}+1\right)^{35}, \forall x \in R\) Since, \(f(x)\) is even function. Hence, the function is not one-one. And \(f(x)>0, y \times \epsilon R\) Hence, the function is not onto. Given, the function is neither one-one nor onto.
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
- Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n^{\text {th }}\) term of A.P. and G.P. respectively thenWBJEE 2024 Easy
- \(\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0\) is true forWBJEE 2021 Easy
- Let \(\alpha\) and \(\beta\) be the roots of \(x^{2}+x+1=0 .\) If \(n\) be a positive integer, then \(\alpha^{n}+\beta^{n}\) isWBJEE 2017 Medium
- Standard deviation of \(n\) observations \(a_{1}, a_{2}, a_{3}, \ldots, a_{n}\) is \({\sigma} .\) Then, the standard deviation of the observations \(\lambda a_{1}, \lambda a_{2}, \ldots, \lambda a_{n}\) isWBJEE 2016 Medium
- In the argand plane, the distinct roots of \(1+z+z^{3}+z^{4}=0(z\) is a complex number) represent vertices ofWBJEE 2014 Medium
- Let the tangent and normal at any point \(P\left(at^2\right.\), 2at), \((a > 0)\), on the parabola \(y^2=4 a x\) meet the axis of the parabola at \(T\) and \(\mathrm{G}\) respectively. Then the radius of the circle through \(\mathrm{P}, \mathrm{T}\) and \(\mathrm{G}\) isWBJEE 2022 Medium
More PYQs from WBJEE
- The most contributing tautomeric enol form of \(\mathrm{MeCOCH}_{2} \mathrm{CO}_{2} \mathrm{Et}\) isWBJEE 2012 Easy
- Centre of mass (C.M.) of three particles of masses \(1 \mathrm{~kg}, 2 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) lies at the point \((1,2,3)\) and C.M. of another system of particles of \(3 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) lies at the point \((-1,3,-2)\). Where should we put a particle of mass \(5 \mathrm{~kg}\) so that the C.M. of entire system lies at the C.M. of the first system ?WBJEE 2021 Easy
- Suppose that the equation \(f(x)=x^{2}+b x+c=0\) has two distinct real roots \(\alpha\) and \(\beta\). The angle between the tangent to the curve \(y=f(x)\) at the point \(\left(\frac{\alpha+\beta}{2}, f\left(\frac{\alpha+\beta}{2}\right)\right)\) and the positive direction of the \(x\) -axis isWBJEE 2014 Hard
- Compound \(X\) is tested and the results are shown in the table.
\(\begin{array}{l|l}\hline \text{ Test } & \text{ Result } \\\hline \text{ Aqueous sodium } & \text{ Gas given off which turns }\\\text{ hydroxide is added, }& \text{ damp red litmus paper }\\\text{ then heated gently. }& \text{ blue. }\\\text{ Dilute hydrochioric }& \text{ Effervescence, gas given }\\\text{ acid is added. }& \text{ off which turns lime water }\\& \text{ milky and acidified }\\& \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \text{ paper green. }\\\hline\end{array}\)
Which ions are present in compound \(X ?\)WBJEE 2016 Medium - The equation of normal of \(x^2+y^2-2 x+4 y-5=0\) at \((2,1)\) isWBJEE 2010 Easy
- If \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}\), then \(k=\)WBJEE 2020 Medium