Page 66 - Mathematics_Form_3

Functions

7. Sketch the graph of the inverse of 11. Find the coordinates of the
x
y = 1 x− 2 ,for 0 ≤≤ 1. turning points of the following
functions:
8. Determine which of the following 2
functions are one-to-one. (a) y = 2 x − 7x + 6
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(b) y = 4 x + x + 1
2
(a) f (x ) = {(x, y ) :
2
(c) y = 2 x + 3x + 4
2
y = x − 4, x ≤ 0}
(b) f (x ) = {(x, y ) : 12. Find the inverse of each of the
2
y = x − 3x + 2, x ≥ 0} following functions and state its
domain and range:
(c) f (x ) = { (x, y ) : y = 8x − 5} _
2

(a) y = √ x − 1 , x ≤ 1.
(d) f (x ) = {(x, y ) : y = 3x + 5} 1
(b) fx = () − x + 3
 x + 2, for x < 0 2
9. If ()gx = 
x
 2, for 0 ≤≤ 2 13. The function h is defined by
(a) find (i) g ( − 1) : hx → x + 2, sketch the graph of
h hence;
(ii) g ( − 4)
(a) State the domain and range of
(iii) g (1.6)
h.
(b) sketch the graph of g(x)
(b) Explain why h does not have
(c) find the domain and range of g.
an inverse.
 x , if x < 0
≤<
10. If ( )gx =  2x − 1, if 1 x 2 (c) The function ()fx = x + 2 for

 x ≥ , c where c is a constant,
 x − 2, if x ≥ 2
state the smallest value of c
(a) find (i) g (1)
for which ()fx has an inverse.
(ii) g (1 . 5) Hence, when c has this value

(iii) g (4) find f − 1 ()x and state its domain Mathematics for Secondary Schools
 21
(iv) g   2   and range.
(b) sketch the graph of g (x)

(c) find the domain and range of
g (x)

(d) is g (x) one-to-one? Why?

Student\s Book Form Three 59

18/09/2025 09:59:05
MATHEMATIC F3 SB.indd 59 18/09/2025 09:59:05
MATHEMATIC F3 SB.indd 59