Find the maximum and minimum values of the fu | vedclass

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Question

(A) Given function is $f(x) = |\sin 4x + 3|$.We know that the range of the sine function is $-1 \leq \sin 	heta \leq 1$ for any $	heta$.Therefore,$-

Vedclass · Accepted Answer

Maximum = $4$,Minimum = $2$

Vedclass · Answer

(A) Given function is $f(x) = |\sin 4x + 3|$.We know that the range of the sine function is $-1 \leq \sin 	heta \leq 1$ for any $	heta$.Therefore,$-1 \leq \sin 4x \leq 1$.Adding $3$ to all parts of the inequality:$-1 + 3 \leq \sin 4x + 3 \leq 1 + 3$$2 \leq \sin 4x + 3 \leq 4$.Since the values in the interval $[2, 4]$ are all positive,the absolute value function does not change the range:$|2| \leq |\sin 4x + 3| \leq |4|$$2 \leq f(x) \leq 4$.Thus,the maximum value is $4$ and the minimum value is $2$.

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

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