Question

Find (f/g) (x). include any restrictions on the domain.
(image attached

Answer 1

`\huge\begin{array}{ccc}A.&\left((f)/(g)\right)(x)=\frac{\sqrt[3]{2x}}{2x+1},&x\\eq-(1)/(2)\end{array}`

Funkction.

We have the functions:

`f(x)=\sqrt[3]{2x}\\\\g(x)=2x+1`

Let's define the domain of the functions:

`D_f:x\in\mathbb{R}\\\\D_g:x\in\mathbb{R}`

Make the function

`\left((f)/(g)\right)(x)=\frac{\sqrt[3]{2x}}{2x+1}`

Let's define the domain of the function:

`D:2x+1\\eq0\\\\2x+1-1\\eq0-1\\\\2x\\eq-1\\\\(2x)/(2)\\eq(-1)/(2)\\\\x\\eq-(1)/(2)`

Answer: A.