Find the maximum and minimum values, if any, of the following function given by,

$f (x) = | s i n 4 x + 3 |$

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Solution

Given function is, $f (x) = | s i n 4 x + 3 |$
We know that $- 1 \leq s i n 4 x \leq 1 \Rightarrow 3 - 1 \leq s i n 4 x + 3 \leq 1 + 3$
$\Rightarrow 2 \leq s i n 4 x + 3 \leq 4 \Rightarrow 2 \leq | s i n 4 x + 3 | \leq 4$
Hence, maximum value of f(x) is 4 and minimum value of f(x) is 2.

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f (x) = | sin 4 x + 3 |

f (x) = | x + 2 | - 1

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f (x) = | sin 4 x + 3 |

Find the maximum and minimum values, if any, of the following functions given by

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