The maximum value of the function f(x) = -|x+ | vedclass

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(C) We know that the absolute value function $|x+1|$ is always non-negative, meaning $|x+1| \ge 0$ for all $x \in R$.
Multiplying by $-1$ reverses th

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) We know that the absolute value function $|x+1|$ is always non-negative, meaning $|x+1| \ge 0$ for all $x \in R$.
Multiplying by $-1$ reverses the inequality: $-|x+1| \le 0$.
Adding $3$ to both sides gives: $-|x+1| + 3 \le 0 + 3$, which simplifies to $f(x) \le 3$.
The maximum value is attained when the term $-|x+1|$ is equal to $0$, which happens at $x = -1$.
Therefore, the maximum value of the function is $3$.

The maximum value of the function $f(x) = -|x+1| + 3, x \in R$ is . . . . . . .

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