(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.

(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 ...

... d) Define a function k: X X that is onto and one-to-one but is not the identity function on X. 7. List all the functions from the three element set {1, 2, 3 ...

One-To-One Functions and Inverses. 1) Which of the given functions is a one-to-one function? ... 2) Which of the given functions is a one-to-one function? ...

... Thus we have N = 3 * 3 * 3 *3 = 3^4 = 81 possible functions from A to B. A one-to-one function means that the element in the range B is matched with at most ...

Proof: Bijective, One-to-one and Onto Functions. 1. Consider f:A->A a one-to-one function. Prove that f is also onto. 2. Consider f:A->A an onto function. ...

... For all one-to-one functions, the inverse function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the ...

... Discrete Functions are scrutinized. (a) Define the function f: R → R by f(x) = x2 - 6. Briefly explain why f is not a 1-1 (one-to-one) function. ...