$f(x)=[\tan^{-1}x]$, where [.] denotes t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

$f(x)=[\tan^{-1}x]$ , where [.] denotes the greatest integer function, is discontinuous at

Options:

$x=\frac{π}{4},-\frac{π}{4}$ and 0

$x=\frac{π}{3},-\frac{π}{3}$ and 0

x = tan 1, −tan 1 and 0

none of these

Correct Answer:

x = tan 1, −tan 1 and 0

Explanation:

f(x) will be discontinuous when $tan^{−1}x = 0$ , 1, −1 as $tan^{−1}x\left(-\frac{π}{2},\frac{π}{2}\right)∀x∈(-∞,∞)$ .

Thus f(x) is discontinuous at x = 0, tan 1, −tan 1.