CUET Preparation Today
The greatest integer function $f(x) = [x]$ is differentiable for all values of |
$x ∈Z$ (set of integers) $x∈R$ (set of real number) $x ∈R-Z$ $x ∈ Q$ (set of rational number) |
$x ∈R-Z$ |
The correct answer is Option (3) → $x ∈R-Z$ The greatest integer function $f(x)=[x]$ has jump discontinuities at every integer. Hence it is: • Not continuous at integers • Therefore not differentiable at integers But it is continuous and differentiable for all non-integer real numbers. So $f(x)$ is differentiable for all $x\in \mathbb{R}-\mathbb{Z}$. |
