Exams › JEE Main › Maths

For the function f(x) = [x]² - [x²], where [y] denotes the greatest integer less than or equal to y, at which points is f discontinuous?

1. at every integer
2. at every integer except 0 and 1
3. at every integer except 0
4. at every integer except 1

Correct answer: at every integer except 1

Solution

f(x) = [x]^2 - [x^2]. At an integer n, f(n)=0. For x slightly above/below an integer the value jumps (e.g. at x=0 the left limit is 1 but f(0)=0). Checking each integer, the left and right limits both equal f only at x=1, so f is discontinuous at every integer except 1.

Related JEE Main Maths questions

• Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).
• A real-valued function f(x) obeys the relation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a is a fixed constant, and f(0)=1. Then the value of f(2a-x) is
• The set of all real values of x for which the function f(x)=(3)/(4-x²)+log₁₀(x³-x) is defined is:
• A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?
• If f(x)=√(1+x²), then which of the following statements is true?
• For the function f(x)=√(x-√(1-x²)), what is its domain?

⚔️ Practice JEE Main Maths free + battle 1v1 →