Cambridge Additional Mathematics

Functions (Chapter 2) 41 So, fwould convert 2 into 2(2) + 3 = 7 and ¡ 4 into 2(¡4) + 3 =¡ 5. This function can be written as: f: ...

42 Functions (Chapter 2) 3 The graph of y=f(x) is shown alongside. a Find: i f(2) ii f(3) b Find the value ofxsuch that f(x)=4. ...

Functions (Chapter 2) 43 11 Given f(x)=ax+ b x , f(1) = 1, and f(2) = 5, find constantsaandb. 12 Given T(x)=ax^2 +bx+c, T(0) =¡ ...

44 Functions (Chapter 2) For example, consider the domains in the table opposite: Click on the icon to obtain software for findi ...

Functions (Chapter 2) 45 Example 6 Self Tutor State the domain and range of each of the following functions: a f(x)= p x¡ 5 b f( ...

46 Functions (Chapter 2) Themodulusorabsolute valueof a real number is its size, ignoring its sign. We denote the absolute value ...

Functions (Chapter 2) 47 Example 8 Self Tutor Solve forx: a j 2 x+3j=7 b j 3 ¡ 2 xj=¡ 1 a j 2 x+3j=7 ) 2 x+3=§ 7 ) 2 x+3=7 or 2 ...

48 Functions (Chapter 2) To draw the graph of y=jf(x)j, any parts of y=f(x) that are below thex-axis are reflected in thex-axis. ...

Functions (Chapter 2) 49 4 Determine whether the following statements are true or false: a If y=f(x) is one-one, then y=jf(x)j i ...

50 Functions (Chapter 2) Algebraically, if f(x)=x^4 and g(x)=2x+3 then (f±g)(x)=f(g(x)) =f(2x+3) fgoperates onxfirstg =(2x+3)^4 ...

Functions (Chapter 2) 51 The domain of the composite of two functions depends on the domain of the original functions. For examp ...

52 Functions (Chapter 2) Consider the three functions given below. Function y=(x+ 2)(x¡1) y=¡2(x¡1)^2 y= 4 x Graph Sign diagram ...

Functions (Chapter 2) 53 EXERCISE 2F 1 Draw sign diagrams for these graphs: abc de f gh i jk l Example 15 Self Tutor Draw a sign ...

54 Functions (Chapter 2) 2 Draw sign diagrams for: a (x+ 4)(x¡2) b x(x¡3) c x(x+2) d ¡(x+ 1)(x¡3) e (2x¡1)(3¡x) f (5¡x)(1¡ 2 x) ...

Functions (Chapter 2) 55 However, not all functions have an inverse function. For example, consider the function y=x^2. The inpu ...

56 Functions (Chapter 2) Example 17 Self Tutor If y=f(x) has an inverse function, sketch y=f¡^1 (x), and state the domain and ra ...

Functions (Chapter 2) 57 Example 18 Self Tutor Consider f:x 7! 2 x+3. a On the same axes, graphfand its inverse functionf¡^1. b ...

58 Functions (Chapter 2) EXERCISE 2G 1 If y=f(x) has an inverse function, sketch y=f¡^1 (x), and state the domain and range of f ...

Functions (Chapter 2) 59 9 Consider the function f(x)=^12 x¡ 1. a Find f¡^1 (x). b Find: i (f±f¡^1 )(x) ii (f¡^1 ±f)(x). 10 Cons ...

PRINTABLE GRAPHS y x (-3 2), O y x y = (x)¦ O y x y = (x)¡¦ O y x -3 1 x -1 O y (2 -5), O x y -4 O x y 2 O x y 5 -5 O x y 1 -1 O ...