Download - F4 C1 Function Tuition Note
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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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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
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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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4.
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SPM QUESTION
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ASSESSMENT
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Topical Test
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