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Question

Let f(x)=cos(cos1(2[x]1)) where [] is the greatest integer function, then

A
Domain of f(x)=R{0,1}
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B
Range of f(x)=[1,1]{0}
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C
Domain of f(x) excludes 3 integral values of x
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D
Range of f(x)={ 2k:kZ{1,0,1}}
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Solution

The correct option is D Range of f(x)={ 2k:kZ{1,0,1}}
f(x)=cos(cos1(2[x]1))
For f(x) to be defined,
12[x]112[x]1+10 and 2[x]110[x]+1[x]10 and [x]3[x]10[x]+1[x]10 and [x]3[x]10[x](,1][3,)x(,0)[3,)
Domain of f(x) excludes 3 integral values i.e. {0,1,2}

Now,
f(x)=cos(cos12[x]1)
y=2[x]1
As [x]Z{0,1,2}
[x]1Z{1,0,1}
Range of f(x) is
{ 2k:kZ{1,0,1}}

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