Question

For the pair of functions find the indicated sum , difference , product or quotient

f(x)= square root of 3x+3 g(x)=1/x

find (f/g) (x)

Answer 1

`\huge\begin{array}{ccc}\left((f)/(g)\right)(x)=x√(3x+3);&x\in[-1,\ \infty)\end{array}`

Functions.

We have:

`f(x)=√(3x+3)`

and

`g(x)=(1)/(x)`

Create the domains:

`D_f:\\\\3x+3\geq0\\\\3x+3-3\geq0-3\\\\3x\geq-3\\\\(3x)/(3)\geq(-3)/(3)\\\\\boxed{x\geq-1\to x\in[-1,\ \infty)}`

`D_g:\\\\x\\eq0\\\\\boxed{x\in\mathbb{R}-\{0\}}`

Solution:

`\left((f)/(g)\right)(x)=(√(3x+3))/((1)/(x))=√(3x+3)\cdot(x)/(1)=x√(3x+3)`