Question

question
$f(x)=\

$$\begin{cases}-6&\\text{for }x < -2\\\\(x + 1)^2 - 3&\\text{for }-2 \\leq x < 1\\\\x&\\text{for }x \\geq 1\\end{cases}$$

$
find $f(-2)$
answer attempt 1 out of 2
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Explanation:

Step1: Match x=-2 to correct piece

The value $x=-2$ satisfies $-2 \leq x < 1$, so use $f(x)=(x+1)^2 - 3$.

Step2: Substitute x=-2 into the formula

Substitute $x=-2$:

$$\begin{align*} f(-2) &= (-2 + 1)^2 - 3 \end{align*}$$

Step3: Simplify the expression

Calculate step-by-step:

$$\begin{align*} f(-2) &= (-1)^2 - 3 \\ &= 1 - 3 \\ &= -2 \end{align*}$$

Answer:

$-2$