Math 99 (Assignments) encoding

1. Supppose f: R ® R and g: R ® R by

   f(x) = 2x + 1

   and

   g(x) =

   x - 1 2

   Show that g o f = id_R and f o g = id_R.

   
   

2. Let R₊ be the set [0,¥), and supppose f: R ® R₊ and g: R₊ ® R are given by

   						__
   f(x) = x2		and		g(x) =	Ö	x

   Is it true that g o f = id_R and f o g = id_R+?

   
   

3. For a function f: X ® X, define f² to be the function f o f. Similarly, define f³ to be f o f², and in general, let fⁿ be defined as f o f^n-1, for any n Î N.

   Let f: R ® R by f(x) = x² - 1. What is f³? (Simplify your answer.)

   
   

4. To be turned in on Wednesday:

   Let A = {-1,0,1} and X = A ´ A. Suppose we define

   f: X ® X   by   f(x,y) = (|x|, (y - x)(x + y)),   and
   g: X ® X   by   g(x,y) = (x², |y| - |x|).

   Are f and g equal? Prove that your answer is correct.

Math 99 (Fall 2002) web pages Created: 28 Oct 2002 Last modified: Oct 28, 2002 7:40:03 PM Comments to: dpvc@union.edu

Assignments