Question

F(x) = 42g(x) = 2x + 3Find () (x). Include any restrictions on the domain.

Answer 1

Determine the function (f/g)(x).

`\begin{gathered} ((f)/(g))(x)=(f(x))/(g(x)) \\ =\frac{\sqrt[3]{4x}}{2x+3} \end{gathered}`

For the real value of the function (f/g)(x), 2x + 3 should not equal to 0. So,

`\text{ 2x + 3 }\\e0`

Simplify

`2x+3\\e0`

to obtain the value of x.

`\begin{gathered} 2x+3\\e0 \\ 2x\\e-3 \\ x\\e-(3)/(2) \end{gathered}`

So x should not equal to -3/2. Thus restiction on the function is,

`x\\e-(3)/(2)`

Answer: Option B.