Question

3-16 A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

12. \(g\left( x \right) = \sqrt[{\bf{3}}]{x}\)

Short answer

The function is one-to-one.

Step-by-step solution

Recall the definition of a one-to-one function

For a one-to-one function, the value of the functionshould not be the same in its domain.

Check for the given function

For the function \(g\left( x \right) = \sqrt[3]{x}\), it can be represented as shown:

\(\begin{aligned}{x_1} &\ne {x_2}\\\sqrt[3]{{{x_1}}} &\ne \sqrt[3]{{{x_2}}}\\g\left( {{x_1}} \right) &\ne g\left( {{x_2}} \right)\end{aligned}\)

Here, all the values of the function are unique.

Therefore, the given function is a one-to-one function.