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Question

# Which of the following statements are correct?1. (fof)(x)=f(x).2. (gog)(x)=g(x) only when x=0.3. (go(fog))(x) can take only three values.Select the correct answer using the code given below

A
1 and 2 only
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B
2 and 3 only
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C
1 and 3 only
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D
1, 2 and 3
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Solution

## The correct option is C 1 and 2 onlyfof(x)=[[x]]=[x]=f(x)gog(x)=sin(sinx))=g(x) at x=0 as g(0)=sin(sin0))=0go(fog)(x)=sin[sinx]=−1 or 0 but not 1 as the highest value of go(fog)(x) can only be sin1 and not 1.Hence, only statement 1 and 2 are correct.

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