Problems from Continuous functions

Development:

Radical functions are continuous within their domain. In this case

$$$x-3 \geq 0$$$ $$$x\geq3$$$ $$$\Rightarrow D(f_x)=[3,+\infty)$$$

Solution:

Therefore $$f(x)$$ is continuous in $$[3,+\infty)$$.

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Development:

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 $$\mathbb{R}-\{-1,1\}$$.

Solution:

The function $$f(x)$$ is continuous in $$\mathbb{R}-\{-1,1\}$$.

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