Question

The range of $f\left(x\right)=-3\cos \sqrt{3+x+x^2}$ is

• A. $[-1,1]$
• B. $[-2,2]$
• C. $[-3,3]$
• D. $[-4,4]$

Answer 1

Answer: (C)

$[-3,3]$

Given $f\left(x\right)=-3\cos \sqrt{3+x+x^2}$
We know that
$-1\le \cos x\le 1\forall x\in R$
So, $-1\le \cos \sqrt{3+x+x^2}\le 1$
$\Rightarrow -3\le 3\cos \sqrt{3+x+x^2}\le 3$
Hence, range of $f\left(x\right)$ is $[-3,3]$