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Natali5045456 [20]
3 years ago
13

Graph the function g(x) = -3 / (x²- 4) . What is the domain of g(x)? Explain your reasoning. Do not completely trust calculator

or computer graphs of this function.
Mathematics
1 answer:
VLD [36.1K]3 years ago
3 0
\bf g(x)=-\cfrac{3}{x^2-4}\\\\
------------------

if the value of the denominator is 0
the fraction becomes "undefined"
so, any value of "x" that makes it 0
is not a valid value for "x", and thus
not part of the domain
let's set the denominator to 0, and find out which one(s) are those if any

\bf x^2-4=0\implies x^2=4\implies  x=\pm\sqrt{4}\implies x=\pm 2\\\\
------------------\\\\
so
\\\\


g(x)=-\cfrac{3}{(-2)^2-4}\to -\cfrac{3}{4-4}\implies g(x)=-\cfrac{3}{0}
\\\\\\

g(x)=-\cfrac{3}{(2)^2-4}\implies g(x)=-\cfrac{3}{4-4}\implies g(x)=-\cfrac{3}{0}\\


\bf -----------------------------\\\\
thus\qquad domain\implies \{x|x\in \mathbb{R};x\ne \pm 2\}
\\\\
\textit{or in interval notation}\implies (-\infty,-2)\cup(2,+\infty)
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