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. $R /\left\{(2 n+1) \frac{\pi}{2}\right\}$ 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 \leq \cos x \leq 1$
$-1-3 \leq \cos x-3 \leq 1-3 $
$ -4 \leq \cos x-3 \leq-2 $
$ \text { Range } \in[-4,-2]$