August 2000
MA214 : DISCRETE MATHEMATICS

QUESTION 4

Total Marks: 15 Marks

• Question 1
• Question 2
• Question 3
• Question 5
• Cover Page

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
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(a) (i) What is meant by saying that a function f : A B is a 1-1 function? [2]
(ii) What is meant by saying that a function g : A B is an onto function? [2]

(b) The functions f : and g : are given by
f(x) =16 +5x , g(x) = x²
Note that is the set of real numbers.
(i) Prove that f is a 1-1 function. [2]
(ii) Is g an onto function? Prove or give a counterexample. [2]
(iii) Calculate f ^-1(x) . [3]
(iv) Calculate g(f(x)) . [2]
(v) Calculate f(g(f(x))). [2]