Question

What is the domain and range of : $y=\sin (x^2-3x+2)$

• A. Domain $=R$ : Range$=[-\frac{1}{2},\frac{1}{2}]$
• B. Domain $=R$ : Range$=[-1,1]$
• C. Domain $=R$ : Range$=[0,1]$
• D. none of these

Answer 1

The correct option is B Domain $=R$ : Range$=[-1,1]$

$y=\sin (x^2-3x+2)$
Domain of $f\left(x\right)$ is all real number $\Rightarrow$ Domain $=R$
Also since $-1\le \sin \theta \le 1$
Therefore range of $f\left(x\right)$ is $[-1,1]$