Question

If $f:R\to S$, defined by $f\left(x\right)=\sin x-\sqrt{3}\cos x$ $+1$, is onto, then the interval of $S$ is

• A. $[0,3]$
• B. $[-1,3]$
• C. $[0,1]$
• D. $[-1,1]$

Answer 1

The correct option is B $[-1,3]$

The given function is onto
$f\left(x\right)=sinx-\sqrt{3}cosx+1$
$\Rightarrow f\left(x\right)=2sin(x-\frac{\pi }{3})+1$
The minimum value $=-1$ and maximum value $=3$
Therefore, S must in the interval $[-1,3]$
Hence, option 'B' is correct.