What is the domain of $f (x) = \frac{x + 4}{x^{2} - 4}$ $f(x)=(x+4)/(x^2-4)$ ?

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What is the domain of $f (x) = \frac{x + 4}{x^{2} - 4}$ $f(x)=(x+4)/(x^2-4)$ ?

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Answer 1 · 2018-04-21T18:13:40

$x \in (- \infty, - 2) \cup (- 2, + 2) \cup (+ 2, \infty)$ $x in(-oo,-2)uu(-2,+2)uu(+2,oo)$

Explanation:

$the denominator of f (x) cannot be zero as this$ $" the denominator of "f(x)" cannot be zero as this"$
$would make f (x) undefined. Equating the denominator$ $"would make "f(x)" undefined. Equating the denominator"$
$to zero and solving gives the values that x cannot be$ $"to zero and solving gives the values that x cannot be"$

$solve x^{2} - 4 = 0 \Rightarrow x = \pm 2 \leftarrow excluded values$ $"solve "x^2-4=0rArrx=+-2larrcolor(red)"excluded values"$

$domain is (- \infty, - 2) \cup (- 2, + 2) \cup (+ 2, \infty)$ $"domain is "(-oo,-2)uu(-2,+2)uu(+2,oo)$
graph{(x+4)/(x^2-4) [-10, 10, -5, 5]}

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What is the domain of $f (x) = \frac{x + 4}{x^{2} - 4}$ $f(x)=(x+4)/(x^2-4)$ ?

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Explanation:

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