Q. If $f:R \rightarrow S$ defined by $f(x) = \sin x - \sqrt{3}\cos{x + 1}$, is onto, then the interval of $S$ is
A) [0, 3]
B) $\lbrack - 1,\ 1\rbrack$
C) [0, 1]
D) $\lbrack - 1,\ 3\rbrack$
Explanation
(d)
Since, $- 2 \leq \sin{x - \sqrt{3}\cos x} \leq 2$
$\Rightarrow - 1 \leq \sin{x - \sqrt{3}\cos{x + 1}} \leq 3$
$\therefore$ Range of $f(x) = \lbrack - 1,\ 3\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.