- Inicio
- Continuity
- Continuous functions
- Ejercicios
Continuous functions
Is this a continuous function $f(x)=\dfrac{5x}{x^2-1}$?
This function is continuous within its domain, because it consists of polynomial functions. And which points are not part of the domain? Those which eliminate the denominator:
$$x^2-1=0$$ $$x^2=1$$ $$x=\pm \sqrt{1}=\pm 1$$
Therefore $f(x)$ is continuous in $\mathbb{R}-\{-1,1\}$.
The function $f(x)$ is continuous in $\mathbb{R}-\{-1,1\}$.
Is this function continuous $f(x)=+\sqrt{x-3}$?
Radical functions are continuous within their domain. In this case
$$x-3 \geq 0$$ $$x\geq3$$ $$\Rightarrow D(f_x)=[3,+\infty)$$
Therefore $f(x)$ is continuous in $[3,+\infty)$.