Question

the equation of the piecewise defined function $f(x)$ is shown. what is the value of $f(1)$?
$f(x)=\

$$\begin{cases}x^{2}+1, -4 \\leq x < 1\\\\-x^{2}, 1 \\leq x < 2\\\\3x, x \\geq 2\\end{cases}$$

$
$f(1)=3$
$f(1)=-1$
$f(1)=2$
$f(1)=-2$

Explanation:

Step1: Identify correct sub-function

For $x=1$, use $f(x)=-x^2$ (since $1\leq x<2$).

Step2: Substitute $x=1$ into the function

$f(1) = -(1)^2$

Step3: Calculate the result

$f(1) = -1$

Answer:

$f(1) = -1$