Consider the following statements :

I. f(t) is an odd function.

Il. g(t) is an odd function.

Which of the statements given above is/are correct?

Question

Question

Direction : Consider the following for the items that follow :

Let f(t) = \(\rm \ln(t+\sqrt{1+t^2})\) and g(t) = tan(f(t)).

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Explanation:

Let f(t) = \(ln (t+\sqrt{1+t^2}\)

f(-t) = \(ln (\sqrt{1+t^2} -t\)

= \(ln( \frac{1}{t+ \sqrt{1+t^2}})\)

= \(-ln(t+\sqrt{1+t^2})\) = -f(t)

∴ f(t) is an odd function

Now g(t) = tan f(t)

Then, g(–t) = tan f(–t)

= –tan (f(t)) = –g(t)

So g(t) is also an odd function

Hence, both statements I and II are correct.

∴ Option (c) is correct

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