Assume that f : ? R is a coordinate function for . (a) Prove that -f is also a coordinate function..

Assume that f :  _ R is a coordinate function for . (a) Prove that _f is also a coordinate function for . (b) Prove that g : _ R defined by gP D f P C c for some constant c is also a coordinate function for . (c) Prove that if h :  _ R is any coordinate function for then there must exist a constant c such that either hP D f P C c or hP D _f P C c.