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Question

If f(x)=(x−1x+1), then which of the following statements is/are correct?

A
f(1x)=f(x)
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B
f(1x)=f(x)
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C
f(1x)=1f(x)
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D
f(1x)=1f(x)
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Solution

The correct options are
B f(1x)=f(x)
D f(1x)=1f(x)
Given, f(x)=x1x+1
Therefore, f(1x)=⎜ ⎜ ⎜1x11x+1⎟ ⎟ ⎟=(1x1+x)=f(x)
and f(1x)=⎜ ⎜ ⎜1x11x+1⎟ ⎟ ⎟=(1x1+x)=(1+x1x)=(1+xx1)=1f(x)
Hence, options B and D are correct.

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