Question

$y={\sin }^{2}x+4\sin x+5$. Then which of the following statements is correct? $(D:$ Domain, $R:$ Range$)$

• A. $D=R$
• B. $D:[2,10]$
• C. $D:[2,10]-\left\{0\right\}$
• D. $R:[2,10]$

Answer 1

The correct option is D $R:[2,10]$

$y={\sin }^{2}x+4\sin x+5$
$\Rightarrow y=({\sin }^{2}x+4\sin x+4)+1=(\sin x+2{)}^2+1$
We know domain of $\sin x$ is R $\therefore$ domain of $y$ is R
Also we know that $-1\le \sin x\le 1$
Thus range of $y$ is $[2,10]$

Hence, option $D$ is correct