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Assume f: A  B and g: B  C are functions. Which are defined?

Assume f: A  B and g: B  C are functions. Which are defined? (1) f  g (2) g  f (3) both (4) neither. Assume f: A  B and g: B  C are functions. What is the domain of g  f ? A (2) B (3) C (4) f (5) g

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Assume f: A  B and g: B  C are functions. Which are defined?

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  1. Assume f: A  B and g: B  C are functions. Which are defined? (1) f  g (2) g  f (3) both (4) neither

  2. Assume f: A  B and g: B  C are functions. • What is the domain of g  f ? • A (2) B (3) C (4) f (5) g • B  A (7) B  C (8) f  g (9) g  f • (10 or 0) A  B

  3. Assume f: A  B and g: B  C are functions. • What is the codomain of g  f ? • A (2) B (3) C (4) f (5) g • B  A (7) B  C (8) f  g (9) g  f • (10 or 0) A  B

  4. What is the next line of this proof? • Let a  A. • Let (x,y) A. • Let a  g  f. • Let (x,y) g  f. • Let a Dom(g  f). • Let (x,y) Dom(g  f).

  5. What is the next line of this proof? • Then a  Dom(f). (2) Then (a, b)  Dom(f) • (3) Then a  g  f. (4) Then (a,b) g  f. • Then a Dom(g  f). (6) Then (a,b) Dom(g  f). • Then a  f. (8) Then (a,b)  f • (9) Then (a,b)  A. (10) Then f(a) = b.

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