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Question

Let f(x)=x1+x and g(x)=rx1x. Let S be the set of all real numbers r such that f(g(x))=g(f(x)) for infinitely many real x. The number of elements in set S is

A
1
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B
2
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C
3
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D
5
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Solution

The correct option is B 2
f(x)=x1+x and g(x)=rx1x
f(g(x))=f(rx1x)=rx1x+rx
g(f(x))=g(x1+x)=rx
Given f(g(x))=g(f(x))
rx1x+rx=rx
r(r1)x2=0
Hence, two solutions are possible.

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