Let f: A->B and g: B->C(adsbygoogle = window.adsbygoogle || []).push({});

a. C_{0}[tex]\subset[/tex]C, show that (g o f)^{-1}(C_{0}))=f^{-1}(g^{-1}(C_{0})).

b. If f and g are injective, show that g o f is injective

c. If g o f is injective, what can you say abuot injectivity of f and g?

d. If f and g are surjective, show that g o f is surjective.

e. If g o f is surjective, what can you say about surjectivity of f and g.

f. Summarize your answers to (b)-(e) in the form of a theorem

I don't know how to do this.... can someone else me..?

Thank You

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Injectivity vs. surjectivity

**Physics Forums | Science Articles, Homework Help, Discussion**