Offline paper
Mathematics · 2016
JEE Main 2016 · 2016-04-03 Offline · Q61
If f(x)+2 f(1/x)=3 x, x ≠ 0, and S ={x ∈ R: f(x)=f(-x)}; then S:
If $\displaystyle f(x)+2 f\left(\frac{1}{x}\right)=3 x, \quad x \neq 0$, and $\displaystyle \mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then S :
Official answer
(3)
contains exactly two elements.
More from Relations and Functions
- Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the value of…2026
- Let the sets A and B denote the domain and range respectively of the function f(x)=1/(√(x -x)), where x denotes the smallest integer greater than or…2023
- If f(x)= log_e((1-x)/(1+x)),|x|<1, then f((2 x)/(1+x^2)) is equal to:2019
- For x ∈(0,3 / 2), let f(x)=√x, g(x)= tan x and h(x)=(1-x^2)/(1+x^2). If φ(x)=((h ° f) ° g)(x), then φ((π)/3) is equal to:2019
- Consider two sets A={x ∈ Z:|(|x-3|-3)| ≤ 1} and B={x ∈ R-{1,2}: ((x-2)(x-4))/(x-1) log_e(|x-2|)=0}. Then the number of onto functions f: A → B is…2026
- Consider functions f: A → B and g: B → C(A, B, C ⊆ R) such that (g ° f)^-1 exists, then:2021
- Let R be a relation on R, given by R={(a, b): 3 a-3 b+√7 is an irrational number }. Then R is2023
- Let f: R-{0} → R be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim_x → 0(1/(α x)+f(x))=β; α, β ∈ R, then α+2 β is equal to2025
JEE Main 2016 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.