# SOLUTION: Let f:X to Y and g:Y to W such that g.f is injective. a) Show f is injective. b) Give an example of functions f and g for which g.f is injective but g is not injective.

Algebra ->  Algebra  -> Functions -> SOLUTION: Let f:X to Y and g:Y to W such that g.f is injective. a) Show f is injective. b) Give an example of functions f and g for which g.f is injective but g is not injective.       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Question 25126: Let f:X to Y and g:Y to W such that g.f is injective. a) Show f is injective. b) Give an example of functions f and g for which g.f is injective but g is not injective. Answer by khwang(438)   (Show Source): You can put this solution on YOUR website! Let f:X to Y and g:Y to W such that g.f is injective. a) Show f is injective. b) Give an example of functions f and g for which g.f is injective but g is not injective. a) f(x) = f(y) --> g(f(x)) = g(f(y)) --> g.f(x) = g.f(y) --> x = y (since g.f is injective) Hence, f is injecitve. b) Set f:{1} --> {1} to be f(x) = x (identity map) and g:{1,2} --> {2} to be g(x) = 2 for x =1,2. We see that g.f:{1}--> {2 } is injective, but g is not. Kenny