Page 48 - Mathematics_Form_3

Functions

Consider a general function defined Example 2.12
by mapping set A onto set B, that
is, f : A → B. Set A is called the domain Find the domain and range of
2
of f and set B is called the range of f. For f (x ) = x + 1.
a given domain A of a function, there is Solution
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a corresponding set B of values called Domain = {x : x ∈ ℝ} .
the range of the function. Range: f (x ) = x + 1 . Set f (x) = y
2
which implies that x = y − 1, which
2
_
Example 2.10 means x = ± y − 1 . Since there is no

√
Find the domain and range of the square root of a negative number, then
function f (x ) = 5x − 1 . y − 1 ≥ 0, giving y ≥ 1. Hence, the
range is {y : y ≥ 1} .
Solution
Domain: The set of all possible values of Therefore, domain = {x : x ∈ ℝ} and
which can give real values of f (x) . In range = {y : y ≥ 1} .
this case, it is the set of all real numbers.
Thus, domain = {x : x ∈ ℝ} . Example 2.13
To find the range of f (x ), first, write
in terms of y, that is x = y + . It is Find the domain and range of
1 _
1 _
5 5 f (x ) = −2x .
2
clear that any value of y from the set of
real numbers will give a unique value Solution
of x. Thus, the range = {y : y ∈ ℝ} . Domain = { x : x ∈ ℝ }.
Since y = −2x , it follows that
2
1
Example 2.11 x = − y
2
Find the domain and range of the Hence, range ={ :yy ≤ } 0.
function f (x ) = x , for − 4 ≤ x ≤ 4.
2
Solution
Exercise 2.3
Domain = {x : − 4 ≤ x ≤ 4} .
To get the range of the function, let Determine the domain and range of the Mathematics for Secondary Schools
y = f (x ), then w rite x in terms of y, following functions defined by:
_
that is, x = ± y . Since there is no
√
square root of a negative number, it 1. f (x ) = 4x + 7, − 10 ≤ x ≤ 10.
_
follows that for the given domain, the 2. f (x ) = √ x , 0 ≤ x ≤ 5.
range = {y : 0 ≤ y ≤ 16} . 1 _
3. f (x ) = , 1 ≤ x ≤ 2.
Therefore, x _
domain = {x : − 4 ≤ x ≤ 4} and 4. f (x ) = √ x
range = {y : 0 ≤ y ≤ 16} . 5. g (x ) = x − 1

Student\s Book Form Three 41

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MATHEMATIC F3 SB.indd 41 18/09/2025 09:58:55
MATHEMATIC F3 SB.indd 41