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Q.

The functions f and g are given by f(x)={x} the fractional part of x and g(x)=12sin⁡[x]π, where [x] denotes the integral part of x. Then range of gof is

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a

[−1,1]

b

{0}

c

{−1, 1}

d

[0, 1]

answer is B.

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Detailed Solution

(gof)(x)=g(f(x))=12sin[{x}]π=0, for all x ∈ R. Hence the range of gof is {0}.
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