Question

Assertion(A): Range of $-3\cos \sqrt{3+x+x^2}$ is $[-3,3]$.
Reason(R) : Maxima and Minima of $\cos x$ does not lie in $[-1,1]$.

• A. A is true, R is true and R is the correct explanation of A.
• B. A is true, R is false
• C. Both A and R are false
• D. A is false, R is true.

Answer 1

The correct option is B A is true, R is false

Assertion (A) : $f\left(x\right)=-3\cos \sqrt{x^2+x+3}$
domain of $f\left(x\right)$
$0\le \sqrt{x^2+x+3}$
$x^2+x+3\ge 0$ (roots are imaginary)
$-1\le \cos \sqrt{x^2+x+3}\le +1$
$\Rightarrow 3\ge -3\cos \sqrt{x^2+x+3}\ge -3$ True.
Reason (R) :
maxima and minima of $\cos x$ does not lie in $[-1,1]$
maximum of $\cos x=1$
minimum of $\cos x=-1$ R is False.
So, B option is correct.