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Finding the Inverses of Toolkit Functions

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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.

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

OpenStax Algebra and Trigonometry 2e, 3.7 Inverse Functions, exercise 14

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.