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Question

If f:RR is an invertible function such that f(x) and f1x are symmetric about the line y=x, then

A
f(x) is odd
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B
f(x) and f1(x) may not be symmetric about the line y=x
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C
f(x) may not be odd
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D
None of these
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Solution

The correct option is A f(x) is odd
Since f(x) and f1(x) are symmetric about the line y=x, if (α,β) lies on y=f(x), then (β,α) lies on y=f1(x).
Therefore, (α,β) lies on y=f(x).
Hence, f(x) is an odd function.

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