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Functions
Chapter summary Revision exercise 2
1. A function from set A to set B is 1. Evaluate the following functions
a relation between the elements when x = 3, x = 0, and x = − 2.
of set A and set B such that (a) ()fx = x + 7
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each element of A is assigned (b) ()fx = 4x − 1
to exactly one element of set B. 1 2
(c) ()fx = x +
3 3
2. In a one-to-one function, each 2. Represent the following
element of set A is assigned to coordinates in the xy-plane:
only one element of set B. A (0, 0), (2, 1), (3, 4), (4, 3), (4, 4)
function that is not one-to-one 3. Represent the following set of
is many-to-one function. ordered pairs in a pictorial
diagram:{(1, −3), (2, 1), (−2, 4),
3. The graph of a function is drawn (−1, 2)}
by setting up a table of values. 4. Sketch the following functions
and state the domain and range of
4. The inverse of a function f(x) is each.
written as f (x ). It is obtained (a) ()fx = 2 x + 1 − 1
−1
by interchanging x and y, and
then making y the subject of the (b) ()fx = − x + 3 + 5
equation. (c) ()fx = x − 2 − 4
5. Some functions such as step 5. Draw the graphs of the following
functions and state the domain and
functions are defined by more (a) () = 2x − 1, for 0 ≤ x < 2
range of each.
than one equation.
Mathematics for Secondary Schools 7. If f − 1 ()x is the inverse of f (x ) , 6. Suppose that a function F is
fx
6. The step function ⌊x ⌋ is the
2
for x ≥
, x
greatest integer function which
0, for 0 ≤
1
x <
is less than or equal to x, and ⌈x⌉
2
(b) ( )fx =
x
, for 1 ≤
x <
is the least integer function which
3, for x ≥
2
is greater than or equal to x.
defined by Fx =
, n where
()
n +
n ≤
x <
1 and n is an integer
then the domain and range of f (x)
are the range and domain of
f − 1 ()x , respectively. such that 4−≤ n < 3. Sketch the
graph of F and hence state its
domain and range.
58 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 58 18/09/2025 09:59:05
MATHEMATIC F3 SB.indd 58
