Final answer:
Cubed root functions are capable of producing all real numbers because the process of cubing preserves the sign of the original number. Both negative and positive real numbers, as well as zero, have real cubed roots.
Step-by-step explanation:
The question revolves around whether cubed root functions can produce all real numbers. Unlike square roots, which only yield real numbers for non-negative inputs, cubed roots can handle both positive and negative inputs because cubing a negative number results in another negative number, thereby preserving the sign. So, when we take the cubed root of any real number, whether it's negative, positive, or zero, we indeed get a real number as an output.
Using a calculator to solve equilibrium problems, one must be familiar with different operations such as square roots, cube roots, and exponential functions. Since these mathematical functions will demand you to work with pure numbers, you should be proficient in performing these functions to achieve correct results.
For example, the cubed root of -8 is -2, because when -2 is cubed (-2 * -2 * -2), it equals -8. Likewise, the cubed root of 27 is 3, because 3 cubed (3 * 3 * 3) equals 27. This demonstrates that for every real number, there is a real cubed root.