Question

The maximum and minimum values of the function $\left|\sin \left(4x\right)+3\right|$ is

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

Answer 1

The correct option is B

$4$, $2$

Explanation for the correct option

Given, $f\left(x\right)=\left|\sin \left(4x\right)+3\right|$

We know that, the maximum value of the $\sin \left(x\right)$ function is $1$and the minimum value is $-1$.
Let $4x=y$. Then,
$\sin \left(4x\right)=\sin y$

Thus, it is clear that the maximum and minimum value of $\sin \left(4x\right)$ will also be $1$ and $-1$ respectively

So, the maximum value will be,
$f\left(x\right)=\left|1+3\right|=4$

And the minimum value will be,
$f\left(x\right)=\left|-1+3\right|=2$

Therefore, the maximum and minimum value of the given function will be $4$ and $2$ respectively.

Hence, option(B) i.e. $4$, $2$ is correct.