Question

evaluate the piecewise function at the given values of the independent variable.
$f(x)=\

$$\begin{cases} 2x + 3 & \\text{if } x < 0 \\\\ 4x + 7 & \\text{if } x \\geq 0 \\end{cases}$$

$
(a) $f(-2)$
(b) $f(0)$
(c) $f(3)$

Explanation:

Step1: Evaluate f(-2) (x<0 case)

Since $-2 < 0$, use $f(x)=2x+3$:
$f(-2)=2(-2)+3$

Step2: Calculate f(-2) value

$f(-2)=-4+3=-1$

Step3: Evaluate f(0) (x≥0 case)

Since $0 \geq 0$, use $f(x)=4x+7$:
$f(0)=4(0)+7$

Step4: Calculate f(0) value

$f(0)=0+7=7$

Step5: Evaluate f(3) (x≥0 case)

Since $3 \geq 0$, use $f(x)=4x+7$:
$f(3)=4(3)+7$

Step6: Calculate f(3) value

$f(3)=12+7=19$

Answer:

(a) $f(-2) = -1$
(b) $f(0) = 7$
(c) $f(3) = 19$