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F(a) = f(b) ⇒ g(f(a)) = g(f(b)), since g is a function ⇒ g f(a) = g f(b), by definition of g f ⇒ a = b, since g f is onetoone Therefore f is onetoone 8 Let f A → B and g B → C Prove that if f is onto B and g is onto C, then g f is onto C PROOF ASSUME f is onto B ie, (∀b ∈ B) (∃x ∈ A) f(x) = b,.

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2 A l g e b r a i c e x p re s s i o n s a r e e v a l u a t e d o r so l v e d from MATHEMATIC MATH1034 at Dokuz Eylül University Tınaztepe Campus.