Question

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

$$\begin{cases}\\frac{x^{2}-4}{x - 2}&\\text{if }x\ eq2\\\\7&\\text{if }x = 2\\end{cases}$$

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

Explanation:

Step1: Evaluate h(3)

Since \(3
eq2\), use \(h(x)=\frac{x^{2}-4}{x - 2}\). Factor \(x^{2}-4=(x + 2)(x - 2)\), then \(h(3)=\frac{(3 + 2)(3 - 2)}{3 - 2}\).
\[h(3)=\frac{(3 + 2)(3 - 2)}{3 - 2}=\frac{5\times1}{1}=5\]

Step2: Evaluate h(0)

Since \(0
eq2\), use \(h(x)=\frac{x^{2}-4}{x - 2}\). Substitute \(x = 0\) into \(\frac{x^{2}-4}{x - 2}\), we get \(h(0)=\frac{0^{2}-4}{0 - 2}\).
\[h(0)=\frac{- 4}{-2}=2\]

Step3: Evaluate h(2)

Since \(x = 2\), use \(h(x)=7\), so \(h(2)=7\)

Answer:

(a) \(h(3)=5\)
(b) \(h(0)=2\)
(c) \(h(2)=7\)