If `f:RRtoS` defined by `f(x)=4sinxx-3cosx+1` is onto, then what is S equal to?

Options

A. `[-5,5]`
B. `(-5,5)`
C. `(-4,6)`
D. `[-4,6]`

Answer

D

Explanation

`f(x)=4sinx-3cosx+1`
To find range of this function, we have to find maximum and minimum values.
We know, for a `sintheta+bcostheta+c`, max value is
`sqrt(a^(2)+b^(2)+c)` and minimum value is `-sqrt(a^(2)+b^(2)+c)`
`:.` Maximum value
`sqrt((4)^(2)+(-3)^(2))+1=sqrt(16+9)+1=5+1=6`
Minimum value `=-sqrt(16+9)+1=-5+1=-4`
`:.` Range, `Sin[-4,6]`