page 05 MARKS 6. Functions, f and g, are given by ( ) cos f x x = + 3 and ( ) g x x = 2 , x∈\. (a) Find expressions for (i) ( ) ( ) f g x and (ii) ( ) ( ) g f x . (b) Determine the value(s) of x for which ( ) ( ) ( ) ( ) f g x g f x = where x ≤ < π 0 2 . 7. (a) (i) Show that ( ) x −2 is a factor of x x x − − + 3 2 2 3 3 2. (ii) Hence, factorise x x x − − + 3 2 2 3 3 2 fully. The fifth term, u5, of a sequence is u a = − 5 2 3. The terms of the sequence satisfy the recurrence relation n n u au + = − 1 1. (b) Show that u a a a = − − − 3 2 7 2 3 1. For this sequence, it is known that • u u = 7 5 • a limit exists. (c) (i) Determine the value of a. (ii) Calculate the limit. [Turn over 2 1 6 2 2 1 3 1