Finding the Inverses of Toolkit Functions

Identify which of the toolkit functions besides the quadratic function are not one-to-one, and find a restricted domain on which each function is one-to-one, if any. The toolkit functions are reviewed in the table. We restrict the domain in such a fashion that the function assumes all y-values exactly once.

$$\begin{array}{ccccc}\text{Constant}& \text{Identity}& \text{Quadratic}& \text{Cubic}& \text{Reciprocal}\\ f\left(x\right)=c& f\left(x\right)=x& f\left(x\right)=x^2& f\left(x\right)=x^3& f\left(x\right)=\frac{1}{x}\\ \text{Reciprocal squared}& \text{Cube root}& \text{Square root}& \text{Absolute value}& \\ f\left(x\right)=\frac{1}{x^2}& f\left(x\right)=\sqrt[3]{x}& f\left(x\right)=\sqrt{x}& f\left(x\right)=\left|x\right|& \end{array}$$

OpenStax, Algebra and Trigonometry 2e · §3.7 Inverse Functions · Example 5