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Consider the following functions.f(x) = x^2 + 2x,g(x) = 3x^2 - 1 Find the domain of (f/g)(x)

Consider the following functions.f(x) = x^2 + 2x,g(x) = 3x^2 - 1 Find the domain of-example-1
User Oxald
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We will have the following:

*First: We have the expression:


(x^2+2x)/(3x^2-1)

Now, we solve for the values in which g(x) = 0, that is:


3x^2-1=0\Rightarrow3x^2=1\Rightarrow x^2=(1)/(3)
\Rightarrow x=\pm\sqrt[]{(1)/(3)}\Rightarrow x=\pm\frac{1}{\sqrt[]{3}}

Thus, the domain of (f / g) (x) is:


\mleft\lbrace x\in R\colon x\\e\mright?\frac{1}{\sqrt[]{3}}\&x\\e-\frac{1}{\sqrt[]{3}}\rbrace

In interval notation:


(-\infty,-\frac{1}{\sqrt[]{3}})\cup(-\frac{1}{\sqrt[]{3}},\frac{1}{\sqrt[]{3}})\cup(\frac{1}{\sqrt[]{3}},\infty)

User Obo
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