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Question

If f(x)=x[x] and g(x)=x0f(t+n)dt nN, then g(52) is equal to

A
f(12)
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B
12
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C
f(32)
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D
f(52)f(5)
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Solution

The correct option is D f(52)f(5)
f(x) is periodic with period 1
g(x)=x0f(t+n)dtg(x)=x0f(t)dtg(x)=f(x)=x[x]g(52)=f(52)=12=f(12)=f(32); also f(5)=0

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