Question

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

Answer 1

Correct Answer - 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.