Find the maximum and minimum values, if any, of the function give… - Vidyadip

Question

Find the maximum and minimum values, if any, of the function given by:
f(x) = |x + 2| -1

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Answer

Given: $\text{f}\text{(x)} = |\text{x} + 2| -1\ \dots\text{(i)}$
Sicen $|\text{x} + 2|\geq0\text{ for all }\text{x}\in \text{R}$
Subtracting 1 from both sides, $|\text{x} + 2| -2\geq -1\ \Rightarrow\ \ \text{f}\text{(x)}\geq-1$
Therefore, minimum value of f(x) is -1 which is obtained when x + 2 = 0 i. e., x = -2
From eq. (i), maximum value of f(x) $\rightarrow \infty $ hence it does not exist.

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