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Question

f:R[1,) and f(x)=ln ( [ |sin2x|+|cos2x| ] ) (where [.] denotes greatest integer function) then which of the following is NOT correct?

A
(RRange of f(x)) is a null set
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B
f(x) is periodic but fundamental period is not defined.
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C
f(x) is invertible in [0,π4]
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D
f(x) is into function.
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Solution

The correct option is C f(x) is invertible in [0,π4]
1|sin2x|+|cos2x|2So, [ |sin2x|+|cos2x| ]=1f(x)=ln (1)=0
it is periodic but fundamental period is not defined.
Also, (RRange of f(x)) is a null set
f(x) is many one and into fucntion.
Hence, f(x) is not invertible.

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