The function f is defined such that (x - B) is a factor of f and the line of symmetry of f's graph is x = -3/4. This means that A = -3/4 and B must be the number such that (-3/4 - B) is a factor of f. Therefore, the values of A and B are -3/4 and 3/4 respectively. The range of f is all real numbers.

1. Starter The function f is defined as follows: Given that (x – B) is a factor of f and x = –¾ is the line of symmetry of the graph of f, find A and B. Hence, state the range of f.

2. Objective: to form composite functions

3. Composition of functions 1 The composite function fg is applied by operating on an input number with the function g then operating on the result with the function f. Find: a) ff(2) = 22 b) gg(–1) = –1 c) fg(3) = 5 d) gf(0) = 4 e) gfg(4) = 1

4. Composition of functions 2 Find the composite functions ff, fg, gf and fgf. Remember: fg means g followed by f.

5. Composition of functions 3 The functions f and g are defined below: Find the value of x such that gf(x) = fg(x).

6. Core 3 & 4 Textbook Exercise 2B Page 26 Questions 10 to 20