Determine the domain of the following functions:
- $$\displaystyle f(x)=\frac{x}{x+3}$$
- $$\displaystyle f(x)=\frac{2x-4}{x^2-9}$$
- $$\displaystyle f(x)=\frac{2}{x}$$
See development and solution
Development:
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We have a rational function, and therefore we must look at the points where the denominator is zero: $$$x+3=0 \Rightarrow x=-3$$$ Therefore $$Dom (f)=\mathbb{R}-\{-3\}$$.
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As in the previous case, we look at the points where the denominator is zero: $$$x^2-9=0 \Rightarrow x^2=9 \Rightarrow x=\pm 3$$$ Therefore $$Dom (f)=\mathbb{R}-\{-3,3\}$$.
- This case is just as the previous ones but obviously the denominator is zero at $$0$$. Therefore, $$Dom(f) = \mathbb{R} - \{0\}$$.
Solution:
- $$Dom (f)=\mathbb{R}-\{-3\}$$
- $$Dom (f)=\mathbb{R}-\{-3,3\}$$
- $$Dom(f) = \mathbb{R} - \{0\}$$