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Consider the following function f: R R defined by f(x) = x3 - 8 .
(a) Note the contrapositive of the definition of one-to-one function given on page 136 of the text is: if a b then f(a) f(b). As we know, the contrapositive is equivalent to, (another way of saying) the definition of one-to-one. Use the contrapositive to explain (no proof necessary) that f is a one-to-one function.

(b) Find f -1. Use the definition of f -1 (definition 9 page 139 of the text) to explain why your solution works.

(c) Compute f f.

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Solution Summary

A horizontal line test is applied.

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