Question 0.1.18: A Sample Rational Function Find the domain of the function f...
A Sample Rational Function
Find the domain of the function
f(x)=\frac{x^2+7 x-11}{x^2-4}.
Here, f(x) is a rational function.We show a graph in Figure 0.21. Its domain consists of those values of x for which the denominator is nonzero. Notice that
x^2-4=(x-2)(x+2)and so, the denominator is zero if and only if x = ±2. This says that the domain of f is
\{x \in \mathbb{R} \mid x \neq \pm 2\}=(-\infty,-2) \cup(-2,2) \cup(2, \infty).
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