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Let f : R rarr[-1,oo] and f(x)= ln([|sin...

Let `f : R rarr[-1,oo] and f(x)= ln([|sin 2 x|+|cos 2 x|])` (where[.] is greatest integer function), then -

A

`f(x)` has range Z

B

Range of `f(x)` is singleton set

C

`f(x)` is invertible in `[0,(pi)/(4)]`

D

`f(x)` is into function

Text Solution

Verified by Experts

The correct Answer is:
B, D
The period of `g(x)=|sin2x|+|cos 2x|" is " pi//4.`
Also, `1le g(x) le sqrt(2).`
Hence `[g(x)]=1 f(x)` is many-one and into function.
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