Question

A company packages colored wax to make homemade candles in​ cube-shaped containers. The production line needs to plan sizes of the containers based on the associated costs. Write a cube root function that tells the side lengths of the​ container, x, in inches for a given​ cost, C.
​x(C) (??????)
nothing ​(Type an expression using C as the​ variable.)

Answer 1

The question is an illustration of inverse functions.

The cube root function is: $\mathbf{ x(C) = \sqrt[3]{C} }$

The question implies that the cost of the cube container is gotten from its volume.

So, the cost function is:

$\mathbf{ C(x) = x^3}$

Next, we calculate the inverse function as follows:

$\mathbf{ C(x) = x^3}$

Rewrite as:

$\mathbf{ C = x^3}$

Take cube root of both sides

$\mathbf{ \sqrt[3]{C} = \sqrt[3]{x^3}}$

$\mathbf{ \sqrt[3]{C} = x}$

Make x the subject

$\mathbf{ x = \sqrt[3]{C} }$

Express x as a function of C

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

Hence, the cube root function is:

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

Read more about inverse functions at:

https://brainly.com/question/10300045