Question

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

$$\begin{cases} \\dfrac{x^2 - 4}{x - 2} & \\text{if } x \ eq 2 \\\\ 3 & \\text{if } x = 2 \\end{cases}$$

\\)
(a) \\( h(3) \\)
(b) \\( h(0) \\)
(c) \\( h(2) \\)

Explanation:

Step1: Evaluate h(3); x≠2, use first formula

First, simplify the rational function:
$\frac{x^2 - 4}{x - 2} = \frac{(x-2)(x+2)}{x-2} = x+2$ (for $x≠2$)
Substitute $x=3$:
$3 + 2 = 5$

Step2: Evaluate h(0); x≠2, use simplified formula

Substitute $x=0$ into $x+2$:
$0 + 2 = 2$

Step3: Evaluate h(2); use second formula

Directly use the given value for $x=2$:
$h(2)=3$

Answer:

(a) $h(3)=5$
(b) $h(0)=2$
(c) $h(2)=3$