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Question

Which of the following represents an odd function?

A
f(x)=(1+ex)2ex
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B
g(x)=sec1(secx)
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C
h(x)=cos(cos1x)
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D
k(x)=cot1(cotx)
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Solution

The correct option is C h(x)=cos(cos1x)
f(x)=(1+ex)2ex
f(x)=(1+ex)2ex
=(1+ex)2exe2x
=(1+ex)2ex
=f(x)
Hence f(x)=f(x). Therefore, f(x) is an even function.
g(x)=sec1(sec(x))
g(x)=sec1(sec(x))
=sec1(sec(x))
=g(x)
Hence g(x)=g(x). Therefore, g(x) is an even function.
h(x)=cos(cos1(x))
h(x)=cos(cos1(x))
=cos(πcos1(x))
=cos(cos(x))
=h(x)
Hence h(x)=h(x). Therefore, h(x) is an odd function.
k(x)=cot1(cot(x))
k(x)=cot1(cot(x))
=cot1(cot(x))
=πcot1(cot(x))
Hence k(x) is neither odd nor even.

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