Question: (15 pts.) Consider the following function f: R \[\xrightarrow{{}}\] R defined by f(x) = x³ - 5 .

(a) Note the contrapositive of the definition of one-to-one function given on page 136 of the text is: if a \(\ne \) b then f(a) \(\ne \) 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 to explain why your solution works. A brief example: Assume f(x) = x³ then f ^-1(x) = \(\sqrt[3]{\text{x}}\) seems to “undo what f does” so it is seems to be f ^-1. We know that f(2) = 8 and

f ^-1(8) = 2 so ?????.

(c) Compute f \[\circ \] f.