18. \( f(x)=x^{3}+5, \quad g(x)=\sqrt[3]{x-5} \)

Did you know that the functions \(f(x) = x^3 + 5\) and \(g(x) = \sqrt[3]{x - 5}\) are inverses of each other? This means if you take an input from one function and plug it into the other, you'll get back the original input! For example, if you calculate \(g(f(x))\), you ultimately get back \(x\), showing that their relationship is like a dance—one leads, the other follows harmoniously! When working with inverse functions like these, a common pitfall is forgetting to apply constraints to the domain and range. Always remember that for the function \(f(x)\), the output will always be greater than or equal to 5, as adding 5 shifts the cubic function up. Conversely, ensure the input for \(g(x)\) starts from 5 upwards so you’ll stay within the real number realm!