Question
Download Solution PDFComprehension
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)).
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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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
Last updated on May 30, 2025
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