Let `f: Xvecyf(x)=s inx+cosx+2sqrt(2)` be invertible. Then which `XvecY` is not possible? `[pi/4,(5pi)/4]vec[sqrt(2,)3sqrt(2)]` `[-(3pi)/4,pi/4]vec[sqrt(2,)3sqrt(2)]` `[-(3pi)/4,(3pi)/4]vec[sqrt(2,)3sqrt(2)]` none of these

Options

A. `[(pi)/(4), (5pi)/(4)] to [sqrt(2), 3 sqrt(2)]`
B. `[-(3pi)/(4), (pi)/(4)] to [sqrt(2), 3 sqrt(2)]`
C. `[-(3pi)/(4), (3pi)/(4)] to [sqrt(2), 3 sqrt(2)]`
D. None of these

Answer

C

Explanation

`f(x)=sqrt(2)"sin"(x+(pi)/(4))+2sqrt(2)`
`or f(x)=sqrt(2)cos(x-(pi)/(2))+2 sqrt(2)`
i.e., `Y=[sqrt(2),3sqrt(2)] and X=[-(3pi)/(4),(pi)/(4)] or [(pi)/(4),(5pi)/(4)]`