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Question

Let g(x)=1+x[x]and f(x)=-1x<00x=01x>0Then for allx, f(g(x)) is equal to


A

x

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B

1

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C

f(x)

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D

g(x)

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Solution

The correct option is B

1


Determine the value of f(g(x))

We know that:

x=x+xx-x=xx[0,1)

Here x is the fractional part of x. Now we have:

f(g(x))=f(1+x-x)=f(1+x)

Here, 1+x>0. So, for x>0,f(x)=1.

Therefore, f(g(x))=1

Hence, option B is the correct answer.


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