Problem 4
A point x is called a fixed-point of a function f if f(x) = x. For example, the function f(x) = x
has infinitely many fixed-points and the function f(x) = x
2 has two fixed-points.
The concept can be extended to functions of more than one variable, if f(x,y) = (x,y). Here the function
maps points on the plane to points on the plane.
Find the fixed-points of the function f(x,y) = (x
3 + 2x
2 - 2, y
2 - xy + x ).
Don't forget to show your
WORK with your solution!
Students, email your solutions to
UNOhighschoolpow@mail.unomaha.edu.
Solutions are due by 11:59PM on Friday October 7th, 2011.
Along with your solution, include your name, your school's name,
the name of your math teacher or math club moderator, and your year in school.
