Question

Find the domain of f/g f(x)=3x^2+x^4+2 g(x)=4x-3

Answer 1

`\left((g)/(f)\right)(x)=(f(x))/(g(x))`

`\text{We have}\ f(x)=3x^2+x^4+2\ \text{and}\ g(x)=4x-3`

`\text{Substitute:}\\\\\left((f)/(g)\right)(x)=(3x^2+x^4+2)/(4x-3)`

`\text{The domain:}\\\\4x-3\\eq0\qquad\text{add 3 to both sides}\\\\4x\\eq3\qquad\text{divide both sides by 4}\\\\x\\eq(3)/(4)`

`Answer:\ \boxed{\text{Domain is the set of all real numbers except}\ (3)/(4)}\\\\\boxed{D=\mathbb{R}-\left\{(3)/(4)\right\}}`