Question

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

Answer 1

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)`