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Question

Let fx=x2+1. Then, which of the following is correct?

(a) fxy=fxfy (b) fxyfxfy (c) fxyfxfy (d) none of these

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Solution

Given: fx=x2+1 .....(1)

Replacing x by y in (1), we get

fy=y2+1

fxfy=x2+1y2+1 =x2+1y2+1 =x2y2+x2+y2+1

Also, replacing x by xy in (1), we get

fxy=x2y2+1

Now,

x2y2+1x2y2+x2+y2+1x2y2+1x2y2+x2+y2+1fxyfxfy

Hence, the correct answer is option (c).

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