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Find the maximum and minimum values, if any, of the following functions given by f (x) = | sin 4x = 3|

(2)Find the maximum and minimum values, if any, of the following functions
given by
(iv) $f (x) = | \sin 4x + 3|$

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Given function is
$f (x) = | \sin 4x + 3|$
We know that value of sin 4x varies from
$-1 \leq sin4x \leq 1$
$-1 + 3 \leq sin4x +3\leq 1 +3\\ 2 \leq sin4x +3\leq 4\\ 2\leq | sin4x +3| \leq 4$
Hence, the maximum value of our function  $f (x) = | \sin 4x + 3|$  is  4  and the minimum value is 2

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