Find the maximum and minimum values of the function
$
f(x) = |\sin(4x) + 3|
$

Q: Find the maximum and minimum values of the function $ f(x) = |\sin(4x) + 3| $

Explanation: Since $-1 \leq \sin(4x) \leq 1$, \[ 2 \leq \sin(4x) + 3 \leq 4 \] \[ \Rightarrow 2 \leq |\sin(4x) + 3| \leq 4 \] \[ \text{Minimum value of } f(x) = 2, \quad \text{Maximum value of } f(x) = 4 \]

Question

Find the maximum and minimum values of the function  
$
f(x) = |\sin(4x) + 3|
$

Accepted Answer

Explanation: Since $-1 \leq \sin(4x) \leq 1$,  
$$
2 \leq \sin(4x) + 3 \leq 4
$$  
$$
\Rightarrow 2 \leq |\sin(4x) + 3| \leq 4
$$  
$$
\text{Minimum value of } f(x) = 2, \quad \text{Maximum value of } f(x) = 4
$$

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