If f(x)= \frac{x}{2}-1 , then on the interval [0,\pi] which one of the following is correct? [NDA II 2017]

Correct Answer is : tan[f(x)],where [.] is the greatest integer function, and 1f(x) are both discontinuous

\tan[f(x)] where [.] is the greatest integer where [.] is the greatest integer function, and 1/{f(x)} are both continuous

\tan[f(x)],where [.] is the greatest integer function, and f^{−1}(x) are both continuous

\tan[f(x)],where [.] is the greatest integer function, and 1/{f(x)} are both discontinuous

\tan[f(x)],where [.] is the greatest integer function, is discontinuous but 1/{f(x)} is continuous

UPSC NDA 2 2017 Mathematics Solved Paper

Question : 80 of 120

Marks: +1, -0

If f(x)=‌‌

−1 , then on the interval [0,π] which one of the following is correct?

[NDA II 2017]

tan[f(x)] where [.] is the greatest integer where [.] is the greatest integer function, and
1
f(x)
are both continuous
tan[f(x)],where [.] is the greatest integer function, and f−1(x) are both continuous
tan[f(x)],where [.] is the greatest integer function, and
1
f(x)
are both discontinuous
tan[f(x)],where [.] is the greatest integer function, is discontinuous but
1
f(x)
is continuous

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