Mathematics · 2019
JEE Main · 8 April 2019, Shift 2 · Q72
Let f:[-1,3] → R be defined as f(x)= {|x|+[x], -1 ≤ x<1; x+|x|, 1 ≤ x<2; x+[x], 2 ≤ x ≤ 3,} where [ t ] denotes the greatest integer less than or…
Let $\displaystyle f:[-1,3] \rightarrow \mathbf{R}$ be defined as
$$f(x)=\left\{\begin{array}{cc}
|x|+[x], & -1 \leq x<1 \\
x+|x|, & 1 \leq x<2 \\
x+[x], & 2 \leq x \leq 3,
\end{array}\right.
$$
where $\displaystyle [\mathrm{t}]$ denotes the greatest integer less than or equal to t . Then, $\displaystyle f$ is discontinuous at:
Official answer
(3)
only three points
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 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.