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A function f is defined by f :x !
3
fix
(a) Given that f :1 ! k , find the value of k.
(b) Given also that f –1: x ! cx + d , find the value of c and the value of d.
f I
155
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k
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2
k
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XII
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34 71 5
Answer (a) k = ........................................... [1]
(b) c = ................... d = ..................
5 [2]
3
21 34 5
2 (a) Given that f(x) = 3x + 5, find f(3).
33
14
5
(b) The function g is defined by g(x) = (2x – 3) (x + k).
gin
Given that g(0) = –15, find
(i)
22 3
k,
(ii) x such that g(x) = 0.
210
0
4 57
0
910
15
221 3
0
4 5
0
3
Ofk
15
2
5
3
k
15
3
2
K
13
K
5
Answer (a) f(3) = ................................ [1]
(b) (i) k = ................................ [1]
(ii) x = ............................... [2]
2
3
f(x) = 2x – 1 .
3
Find an expression for f –1(x).
Y
2x I
3
34 221 1
271 34 1
71 34 1
2
F x 32 1
Answer f–1(x) = .............................................[2]
4 It is given that f(x) = 3x – 5.
Find
b
3141 5
17
(a)
f(– 4),
(b)
the value of t, given that f(t) = 10,
(c)
f –1(x),
(d)
f –1(4).
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10
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fly
71
35
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3
30
31 5 10
21
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31 15
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fly
745
3
3
Answer (a) f(– 4) = ...............................[1]
(b) t = ...................................... [1]
(c) f –1(x) = ...............................[1]
(d) f –1(4) = .............................. [1]
3
5
(a) f(x) = (x + 2)(2x – 1).
Evaluate f(5.5). 5.5 2 215.57 1
(b) g(x) = 13 (2x – 1).
Find g–1 (5).
4 512
1
1
34 221
34 1 221
2
gin
6
75
7 5 10
gin 32 1
151 3152 1
g
8
Answer (a) f(5.5) = .......................................[1]
1
34
(b) g–1(5) = ......................................[2]
3211
(a) Given that f(x) = x2 – 2px + 3, find
(i) f(–2), giving your answer in terms of p,
(ii) the value of p when f(–2) = f(0).
g
(b) Given that g(y) = y2 – 1, find g(a – 1).
Give your answer in its simplest form.
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Answer (a) (i) f(–2) = .............................[1]
(ii) p = ...................................[1]
(b) g(a – 1) = .............................[2]
I
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4
7
4 53 9
Given that f(x) = 5x 3– 4 , find
Fmean
(a) f(1 15 ),
34 54 4
(b) f–1(x).
34 4 521
f it
4
21 3
544 4
3
f 1 7 373 4
3
Answer (a) ....................................................[1]
(b) ....................................................[2]
8
f(x) = 3 – x .
2
It is given that
2 3
Find
91 122 6
3
(a) f(–9),
4
(b) f–1(x).
FIN
24
3 221
4 32
9
6
24 3 71
Answer (a) .................................................[1]
24 3
(b) f–1(x) = .....................................[1]
3 22
It is given that f(x) = 5x + 2.
Find
51 27 2
(a) f (–2),
10 2
8
(b) f –1(x).
4
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52
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Answer (a) ............................................[1]
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(b) f–1(x) = ...............................[1]
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10 Given that f (x) = 4x + 3 , find
2x
(a) f(3) ,
(b) f –1 (x) .
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3
4 4
2 4 42
3
x 24 4
3
x
24 4
f x
23 4
Answer (a) f(3) = ..................................[1]
(b) f –1 (x) = ..............................[2]
11 It is given that f(x) = 12 – 5x.
Find
(a) f(4) ,
12 5147
12 20
8
8
Answer (a) f(4) =............................. [1]
(b) the value of x for which f(x) = 17,
12 521 17
17
12 5
5 52
x
(c) f –1(x).
Answer (b) x = ................................ [1]
4
12 571
2
5
4
12
FIN
52
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12 y
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12 2
5
Answer (c) f –1(x) = ......................... [2]
6
12 Given that f(x) = 4x – 7, find
1
(a) f   ,
2
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5
Answer (a) f 
5
1
= ...........................[1]
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(b) the value of p when f( p) = p.
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4p
P
38 7
p
p
7
4p p
Answer (b) p = ................................[2]
13
Given that f(x) = 5 – 2x, find
3x
5
(a) f(–2),
21 2
31 2
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I
3
3
These are all same
3
Answer (a) f(–2) = ........................ [1]
4
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3
5
2x
22
5
21 34 2
5
(b) f –1(x).
3
321
4
4
x
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5
fink 32 2
Answer (b) f–1(x) = ........................ [2]
7
14 f(x) = 6 – x
2
(a) Find f(5).
It 3 151 3
6 2.5
3.5
Answer (a) ...................................... [1]
(b) Find f –1(x).
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g
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12
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2
216 y
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12 28
fire
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24
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12
2 12 24
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12 2x
Answer (b) f –1(x) = ........................ [2]
8
15
It is given that h(x) = 2x − 5 and g(x) = x3 − 2 .
Find
(a) h(4),
(b) g−1(x),
3
2141 5
y
3 z
YX 2
3
R
........................................ [1]
Answer
........................................ [2]
3
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Answer
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3
22
(c) the value of t such that h(t) = g(3).
22 5 33 2
It 5
3
It
8
t
4
Answer t = .................................. [2]
9
16
2x + 3
–1
5x , find f (x) .
Given that f(x) =
I's
524 22 3
SRY 2n
3
N
3
5y 2
N
5
2
5
2
F
Answer f –1(x) = ................................... [2]
17
It is given that f(x) = 3 2+ x .
(a) Find f(–3).
3
31
3
4
O
Answer
O
.......................................
[1]
(b) Find f –1(x).
4 311
24 3 71
3
fix
24
2
3
3
22 3
Answer f –1(x) = ......................... [1]
10
f(x) = 6x2 – x + 3
18
(a) Find
(i) f(2),
61212 2
3
24 2 3
25
25
Answer f(2) = ........................... [1]
(ii) f(–1),
61 1721 17 3
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Answer f(–1) = .........................
[1]
(iii) the values of x for which f(x) = 5.
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6,442
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fix
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Answer x = ............. or .............[2]
(b) Write down and simplify an expression for f(a + 1).
6 2
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5
3
3
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6 a72 a 1
th
602 129 6
Ga til a
a
a
1 3
1
3
8
Answer f(a + 1) = ......................................... [2]
0
11
f(x) = x3 – 4
19 (a)
Find
2
(i) f(–2),
3
4
8 4
12
Answer f(–2) = .........................
12 [1]
(ii) f –1(x).
y 23
4 4 23
x
y
4
3
x
fin
(b)
4
y 4
Yn
4
3
set 4
Answer f –1(x) = ................................. [1]
g(y) = y2 – 3y + 1
Write down and simplify an expression for g(a – 2).
gfa
2
a
272 3
191 2 a 2
2
a
2
a
4 at 4
d
Ta t 11
2
3a
I
3 a tb
I
6 1
Answer g(a – 2) = ........................................ [2]
12
20
f(x) =
(a) Find f –1(x).
x+3
2
Y 213
3
2
24
2
fly
24 3
2n 3
Answer f –1(x) = .......................
2n 3 [1]
(b) Given that f(–9) + f(t) = A + Bt , find the values of A and B.
3
92
tf
9 3 1 3
Igt
It
32
3
BE
A
Answer A = ...................................
I
B = .............................. [2]
21
f(x) = 5 + 3x
(a) Evaluate f !–
1
.
2
"
5
3
12 7,5 3
10 3
5 1.5
35
Answer
(b) Find f –1(x).
3
..................................... [1]
4 5 321
Y 5 311
x
y
thy
71 5
3
Answer f –1(x) = ........................ [1]
13
22
f(x) =
(a) Find f(4) .
7 - 3x
2x
7
7247
f
Answer
(b) Find f –1(x) .
................................................ [1]
5g
In
Zoey 7
32
Ky
32
7
N 2
3
7
2
y
n
Ly 3
FG
It
Answer f –1(x) = ................................... [2]
f(x) = 2x – 6
23
(a) Evaluate f `- 21 j .
6
214
1 6
Answer
(b) Find f −1(x).
7
............................................... [1]
6
Y 2n
Y tf 2K
x
fin
TI
of
Rtf
Answer f −1(x) = .................................. [1]
14
24
f^xh = 2 - 3x
Find
(a) f ^-5h,
2 15
2 31 5
17
Answer f ^-5h = ............................................. [1]
(b) f -1 ^xh.
2 3N
4
3kt y
2
371
2 Y
X
Y
3
Fini 23
Answer f -1 ^xh = ............................................. [2]
f ^xh = 2 ^x - 3h
25
(a) Evaluate f ` 12 j .
(b) Find f -1 ^xh.
1 37
4 212
4 2
2
121 245
5
Answer
5
.............................................
[1]
Answer
f -1 (x) = ............................. [1]
3
6
4 6 271
71
Ytb
fine if
15
f ^xh = 5 + x 2
26
Find t given that f ^3 - th = 9.
9
5 13 t
3 t
4
3 t
154
t
I 2
3
3 t
2
3
tt2
2
t
3
3
t
t
2
t
5
Answer
5
I
t = ..............
or ............... [3]
27
f(x) = 1 + 4x
2
(a) Find f `- j .
5
8 57 3
41
Answer ................................................. [1]
(b) Find f –1(x).
y
1 42
x
YI
Y 1 42
fin
Answer f –1(x) = ................................................. [1]
16
28
f (x) = 2x - 9
(a) Find f c- m.
3
4
9
241
3
3 9,1
212
218
Answer ............................................. [1]
(b) Find f –1(3).
ft3 321 122
4 22 9
4 9 221
x
6
ytf
Fy say
Answer ............................................. [2]
29 (a) The table shows the values of the function f^xh for some values of x.
x
1
f ^xh
5
7 III Y
É
2
3
4
5
7
9
11
13
cist is
grad 31
Express the function f ^xh in terms of x.
58
egotist
5 101 1 121
y 5
Y 22 2 5
t
(b)
g ^xh =
(i) Evaluate g ^-2h.
(ii) Find g ^xh.
mix xp
212 17
Answer f ^xh = ................................
22 3 [1]
271 3
-1
y y
2
8
y
321
8 - 3x
2
21
8
7
142
Answer ........................................... [1]
23N
32
8
24 8 371
21
8
321 24 8
fire
24
324
8 2n
3
Answer g -1 ^xh = ........................... [2]
17
30
f (x) =
(a) Evaluate f (– 12 ).
3
3-x
10
3
3
It
0.35
Answer .......................................... [1]
y
3
toy
3 x
(b) Find f –1(x).
Xt
n
10
toy
31
fin
3
3
104
3
10k
3
102
Answer f –1(x) = .......................................... [2]
f(x) = 4 + 3x
31
1
(a) Find f b- 2 l.
2
212means
E
4 3
E
1
152
8
215
I
Answer .......................................... [1]
(b) Find f -1(5).
y 4 371
Y 4 32
a
f 5 531
YY
f n XI
Answer .......................................... [2]
18
32
32 (a) Solve
24
6
5
=
.
x+1 x-3
66 37 56 11
52 5
Gn 521 18 5
62 18
g (x) = x 2 + 1
f (x) = x - 3
(b)
23
Answer x = ..................................... [2]
23
71
5 3
(i) Find f(− 5) .
8
8
Answer ........................................... [1]
(ii) Find m given that g (m - 3) = 17.
Im 3
2
m 35
33
f (x) =
m 3
17
1
1,16
m 3
14
m
3
4
me
16
m 3
4
I [3]
7
Answer m = ...............
or ...............
3x - k
4
(a) Given that f(11) = 7, find the value of k.
31111,4 7
33 1
28
(b) Find f –1(x).
4 324
5
49 3
5
44 5 321
33 28 4
33 28 k
5 K
Answer k = ..................................... [2]
x 44 5
3
fly
42 5
3
Answer f –1(x) = ............................. [2]