Find the domain of the following rational function. $$ h(x)=\frac{x+2}{x^{2}-4} $$

Question

UpStudy AI · Accepted Answer

The domain of $$h(x)$$ is $$(-∞, -2) \cup (-2, 2) \cup (2, ∞)$$. To find the domain of the rational function $$ h(x) = \frac{x+2}{x^2 - 4}, $$ we need to determine where the function is defined. A rational function is undefined wherever the denominator is equal to zero. First, we set the denominator equal to zero and solve for $$x$$: $$ x^2 - 4 = 0. $$ This can be factored as: $$ (x - 2)(x + 2) = 0. $$ Setting each factor equal to zero gives us the solutions: $$ x - 2 = 0 \quad \Rightarrow \quad x = 2, $$ $$ x + 2 = 0 \quad \Rightarrow \quad x = -2. $$ Thus, the function $$h(x)$$ is undefined at $$x = 2$$ and $$x = -2$$. The domain of $$h(x)$$ consists of all real numbers except these two points. In interval notation, we can express the domain as: $$ (-\infty, -2) \cup (-2, 2) \cup (2, \infty). $$ Therefore, the domain of the function $$h(x)$$ is $$ \boxed{(-\infty, -2) \cup (-2, 2) \cup (2, \infty)}. $$

Find the domain of the following rational function. \[ h(x)=\frac{x+2}{x^{2}-4} \]

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Find the domain of the following rational function. \[ h(x)=\frac{x+2}{x^{2}-4} \]

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions