Mathematics · 2021
JEE Main · 26 February 2021, Shift 1 · Q74
Let f be any function defined on R and let it satisfy the condition: |f(x)-f(y)| ≤|(x-y)^2|, ∀(x, y) ∈ R If f(0)=1, then:
Let $\displaystyle f$ be any function defined on R and let it satisfy the condition :
$$|f(x)-f(y)| \leq\left|(x-y)^2\right|, \forall(x, y) \in \mathbf{R}
$$
If $\displaystyle f(0)=1$, then :
Official answer
(1)
$\displaystyle f(x)>0, \forall x \in \mathbf{R}$
More from Continuity and Differentiability
- If f(x)= {∫_0^x(5+|1-t|) dt, x>2; 5 x+1, x ≤ 2}, then2021
- If the function f(x)= {1/x log_e((1+x/a)/(1-x/b)), x<0; k, x=0; (cos^2 x- sin^2 x-1)/(√(x^2+1)-1), x>0} is continuous at x=0, then 1/a+1/b+4/k is…2021
- Let f: R → R be a differentiable function that satisfies the relation f(x+y)=f(x)+f(y)-1, ∀ x, y ∈ R. If f^′(0)=2, then |f(-2)| is equal to ____.2023
- Let [x] denote the greatest integer function and f(x)= max {1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤ 2. Let m be the number of points in [0,2], where f is not…2023
- Consider the function f(x) =(P(x))/(sin (x-2)), x ≠ 2 =7, x=2 where P(x) is a polynomial such that P^′ ′(x) is always a constant and P(3)=9. If f(x)…2021
- The function f(x)= {(π)/4+ tan^-1 x, |x| ≤ 1; 1/2(|x|-1), |x|>1} is:2020
- Let [t] denote the greatest integer ≤ t and lim_x → 0 x[4/x]=A. Then the function, f(x)=[x^2] sin (π x) is discontinuous, when x is equal to:2020
- Suppose that the function f(x)= {x^2-[x]+2 a; x<-1; 4 x+5-b; -1 ≤ x<2; 3 x^2+6[x]-2 a; x ≥ 2} is continuous on (-2,3) for some values of a and b…2021
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.