Rational functions

Determine the domain of the following functions:

  1. $\displaystyle f(x)=\frac{x}{x+3}$
  2. $\displaystyle f(x)=\frac{2x-4}{x^2-9}$
  3. $\displaystyle f(x)=\frac{2}{x}$

  1. 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 $Dom (f)=\mathbb{R}-\{-3\}$.

  2. 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 $Dom (f)=\mathbb{R}-\{-3,3\}$.

  3. This case is just as the previous ones but obviously the denominator is zero at $0$. Therefore, $Dom(f) = \mathbb{R} - \{0\}$.

  1. $Dom (f)=\mathbb{R}-\{-3\}$
  2. $Dom (f)=\mathbb{R}-\{-3,3\}$
  3. $Dom(f) = \mathbb{R} - \{0\}$
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