Definition of one-to-one function

Question

Discussion:

Q: 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 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.