Question

F(x) = √3x

Answer 1

The domain of the function is $(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$ . $x \ne -\frac 25$

How to determine the domain and the restrictions?

The attached image represents the complete form of the question

The functions are given as:

$f(x) = \sqrt[3]{3x}$

g(x) = 5x + 2

The function (f/g)(x) is calculated using:

$(\frac{f}{g})(x) = \frac{f(x)}{g(x)}$

This gives

$(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$

The denominator cannot be 0.

So, we have:

$5x + 2 \ne 0$

Solve for x

$x \ne -\frac 25$

Hence, the domain of the function is $(\frac{f}{g})(x) = \frac{\sqrt[3]{3x}}{5x + 2}$ . $x \ne -\frac 25$

Read more about domain at:

brainly.com/question/1770447

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