MAT137Y1 Lecture Notes - Lecture 5: Injective Function

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: Thaddeus Janisse

Document Summary

A function f : (a, b) r is injective on (a, b) if x (a, b), Y (a, b), x 6= y f(x) 6= f(y). If c does not= 0, show that the function f(x) = cx is injective on all of r. Let x and y be arbitrarily chosen and . If f : r r and g : r r are both injective functions, then their composition f g : r r is also injective. Result: the composition f g is also injective; that is, f(g(x)) = f(g(y)) implies that x = y. Let f : r r and g : r r be two functions. If the function f g is injective, then g is injective. Hypotheses: f g is injective; that is, f(g(x)) = f(g(y)) implies that x = y. Want to show: g is injective; that is, g(x) = g(y) implies that x = y.