F4 C1 Function Tuition Note

8/13/2019 F4 C1 Function Tuition Note

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F4 Additional Mathematics Note Chapter 1 Functions

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1.1 Relations

CHAPTER Functions


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More example


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1.1 b Domain, Codomain, Objects, Images and Range


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1.

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2.


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1.1 c Types of relations


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Example


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1.2 Functions

1.2 a Definition of functions


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Exercise


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1.2 b Express function using function notation

1.2 c Domain, Range, Objects and Images of a Function


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Exercise :


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`1.2 d To Solve Problems Involving Functions


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Exercise :


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4. Given that f(x) = , f(3) = -5 and f(-5) = -1, find

a) the value of a and b

b) the value of x such that the function f is undefined.

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5. The arrow diagram shows the function f(x) = px + qx 2. Find

a) p, q

b) the values of x such that mapped onto themselves

6. Given that f(x) = , x 2, f(1) = 2 and f(3)= 4, find

a) the value of p and q.

b) the values of x such that f(x) = x

-1

-2-5

-16

x px + qx 2

f


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1.3 Absolute Value Functions

1. The absolute value of x is written x and it is read as the modulus of x

2. The definition of x is

x, if x 0 x =

- x , if x


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Exercise :

1. Given the function f : x x-4, find the values of x such that f(x) = 9

2.


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3.


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More example


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6. The functions f and g are defined by f(x)= mx + 2 and g(x) = kx -3 respectively. If fg=gf , find the relationbetween m and k . If m= 5, find the value of x that satisfies each of the following equations.

a) f 2 = f b) g 2=g


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Exercise :


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4. The functions f and g are defined by f(x) = (x + 1) 2 and g(x) = x-2 respectively.

Find a) the composite function fg and gf

b) the values of x if i) fg =9 ii) gf = 14

c) the value of x if fg=gf

1.4 b To Find the Related Function Given the Composite Function and One of the Functions

Example :

1.The function f is defined by f(x) = 2x +4. Another function g is such that fg(x) = 3x -8. Find the function g

2. The function f is defined by f(x) = x-2 . Another function g is such that gf(x) = , x .

Find the function g


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2.

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4.


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1.

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2.

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3.


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4.

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SPM QUESTION


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ASSESSMENT


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Topical Test


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F4 C1 Function Tuition Note