Question

f(x) = 332g(x) = 5x + 2Find(4) (2). Include any restrictions on the domain.

Answer 1

$f(x)/g(x)\text{ = }\frac{\sqrt[3]{3x}}{5x\text{ + 2}},\text{ x }\ne-\frac{2}{5}\text{ (option D)}$

Explanation:

(f/g)(x) = f(x)/g(x)

$\begin{gathered} f\mleft(x\mright)=\sqrt[3]{3x} \\ g(x)\text{ = -5x + 2} \end{gathered}$$f\mleft(x\mright)/g\mleft(x\mright)\text{ = }\frac{\sqrt[3]{3x}}{5x\text{ + 2}}$

We need to find the restriction. That is a number that will make the expression undefined.

That number will cause the denominator to be equal to zero.

we make the denominator to be equal to zero:

5x + 2 = 0

5x = -2

x = -2/5

The number that will make the expression undefined, x = -2/5

$f(x)/g(x)\text{ = }\frac{\sqrt[3]{3x}}{5x\text{ + 2}},\text{ x }\ne-\frac{2}{5}\text{ (option D)}$