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one-to-one function

(a) Define the function f: R-->R by f(x) = x3 + 4. Briefly explain why f is a 1-1 (one-to-one) function. No proof necessary, just
an explanation in some detail (b) Is the function g: R -->Z defined by g(n) = [n/2]a one to one function?
(Be careful,[n/2]means the ceiling function.) Explain. (c) Briefly explain what f-1 means in general and then find f-1for the function f
in part a.


Solution Preview

(a) One way to determine that f(x) is a one-to-one function is to graph the function. The graph of f(x) is the graph of y=x^3 shifted up 4 units. This function passes the horizontal line test. That is, any horizontal line that we can ...

Solution Summary

One-to-one functions are examined.