(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 ...

... Show that f is one-to-one onto ⇔ there exists a mapping g of X into itself such that fg = gf = ix . ... Why? Topology Sets and Functions (XXXIX) Functions. ...