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Question

If f:RR and g:RR are defined by f(x)=|x| and g(x)=[x3] for xR, then
g(f(x)):{85<x<85} is equal to

[.] is Greatest integer function

A
{0,1}
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B
{1,2}
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C
{3,2}
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D
{2,3}
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Solution

The correct option is C {3,2}
Given that, f(x)=|x| and g(x)=[x3]
For 85<x<85,0f(x)<85
Now, for 0<f(x)<1,
g(f(x))=[f(x)3]
=33f(x)3<2
Again, for 1<f(x)<1.6
g(f(x))=2
2f(x)3<1.4
Hence, required set is {3,2}

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