Question

The domain and range of $y(x)=\cos x-3$ are respectively

• A. $R$ and $[-1,1]$
• B. $R$ and $[-4,-2]$
• C. $R/\{0\}$ and $[0,1]$
• D. $R/\left\{(2n+1)\frac{\pi }{2}\right\}$ and $[-1,1]$

Answer 1

Answer: (B)

$y(x)=\cos x-3$
Domain of $\cos x$ is $R$.
By subtracting 3 from $\cos x$ there will not be any change in the domain.
So, domain of $y(x)$ is $R$.
$-1\le \cos x\le 1$
$-1-3\le \cos x-3\le 1-3$
$-4\le \cos x-3\le -2$
$\text{ Range }\in [-4,-2]$