Problems from Domain of a function

Development:

1) The first function is a polynomial of second degree. Therefore, $Dom(f)=\mathbb{R}$

2) In this case, we need to check that the inside expression is positive, which is: $x+4\ge 0\Rightarrow x\ge -4$.

Therefore, $Dom(f)=[-4,+\mathrm{\infty })$.

3) Finally, since it is a rational function we have to verify that the denominator is not zero (since it is not possible to divide by $0$): $$x+1=0$$ $$x=-1$$ Therefore, $Dom(f)\mathbb{R}-\{-1\}$

Solution:

1) $f(x)=x^2-2$

$Dom(f)=\mathbb{R}$

2) $f(x)=\sqrt{x+4}$

$Dom(f)=[-4,+\mathrm{\infty })$

3) $f(x)={\displaystyle \frac{1}{x+1}}$

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

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