Problems from Continuous functions

Development:

Radical functions are continuous within their domain. In this case

$$x-3\ge 0$$ $$x\ge 3$$ $$\Rightarrow D(f_x)=[3,+\mathrm{\infty })$$

Solution:

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

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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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