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Mathematics for IGCSE & O level - Functions (Section 2)

1
If f(x) = 3x + 2, then which is f^-1(x)?
Answer
(B)
(x-2)/3
2
If f(x) = 3x - 2, what is the value of x if f(x) = 7?
Answer
(B)
13/3
3
Given that f(x) = 5x + 2, solve the equation f(x) = 12
Answer
(A)
2
4
If g(x) = 6 - 2x, what is g(-3)?
Answer
(C)
12
5
If f(x) = x/3, what is the value of f^-1(9)?
Answer
(C)
27
6
f(x) = 2x-3. Find x when f(x) = 5.
Answer
(C)
2
7
Which of the following are key concepts when working with composite functions?
Answer
A
B
8
If f(x) = 2x - 3 and g(x) = x + 1, find g(f(2))
Answer
(A)
2
9
If f(x) = 2x - 4, then f^-1(x) = ?
Answer
(A)
(x+4)/2
10
If f(x) = 2x, then f(x+3) is:
Answer
(C)
2x+6
11
If g(x) = 2x-1, find g(0).
Answer
(B)
-1
12
Given g(x) = 7-3x, what is the value of x if g(x) = 0?
Answer
(A)
7/3
13
Given f(x) = x + 4, find f(2)
Answer
(D)
8
14
If f(x) = x - 7, what is f(10)?
Answer
(A)
3
15
Which of the following equations correctly represents the inverse of the function f(x) = 5x - 5?
Answer
(B)
f^-1(x) = (x + 5)/5
16
What is the process for finding the inverse of a function?
Answer
A
B
C
17
If h(x) = 3x^2 - 1 and h(x) = 11, what is a possible value of x?
Answer
(C)
3
18
If f(x) = x^2, what is f(f(x))?
Answer
(A)
x^4
19
If f(x)= 2x and g(x) = x+1, then what is g(f(x))?
Answer
(A)
2x+1
20
If f(x) = 2x + 1, what is f(0)?
Answer
(B)
1
21
When finding the inverse of a function, what algebraic operation is the same?
Answer
(D)
x with f(x)
22
Which of the following represents a function?
Answer
(B)
A relationship where each input has only one output
23
If the range of f(x) is {1, 2, 3}, which set of values could be the domain of f^-1(x)?
Answer
(A)
{1, 2, 3}
24
What is the definition of the range of a function?
Answer
(B)
The set of all y-values.
25
Functions can be described as one-to-one or many-to-one. Which of the following statements are true?
Answer
A
B
D
26
In a mapping diagram, what is the purpose of the arrows?
Answer
(C)
To show the relationship between the input and output values
27
What is the general form of an inverse function?
Answer
(C)
f^-1(x) = y
28
For the function f(x) = 3x+2, what is f(h(x)) if h(x)= x-1?
Answer
(D)
3x-5
29
Given the function g(x) = 5x + 2, what is the range for the domain {-1, 0, 1, 2, 3}?
Answer
(A)
{-3, 2, 7, 12, 17}
30
If f(x) = 3x + 1, what operation maps x to 3x + 1?
Answer
A
B
31
If g(x) = 6 - 2x, find g(t).
Answer
(C)
6 - 2t
32
If f(x) = 3(2x-5), where x = 0, what is f(x)?
Answer
(B)
15
33
If f(x) = x^2 + 3, find f(-2).
Answer
(B)
1
34
If f(x) = x^2 + 3 and the domain is {-1, 1}, what is the range?
Answer
(C)
{3, 4}
35
If f(x) = 3(2x-5), where f(x) = 15, what is x?
Answer
(C)
10
36
If g(x) = 5x + 2, what is the range for the domain {-1, 0, 1, 2, 3}?
Answer
(B)
-3, 2, 7, 12, 17
37
When g(x) = 7 - 3x and x = -5, what is g(x)?
Answer
(B)
-8
38
Which of the following steps are involved in finding an inverse function, f⁻¹(x)?
Answer
A
B
C
39
If f(x) = x^2 and g(x) = x + 2, what is f(g(x))?
Answer
(B)
(x+2)^2
40
Which of the following are correct concerning the function f(x) = x²?
Answer
A
C
D
41
Given the function f(x) = 4x + 3, what is the value of f⁻¹(3)?
Answer
(A)
0
42
If the domain is {0,1}, and the range is {0, 1}, what type of function is f(x) = x²?
Answer
(B)
Quadratic
43
Which of the following are important in finding an inverse function?
Answer
A
C
D
44
If g(x) = x/4, and g(x) = 2, what is x?
Answer
(A)
8
45
If g(x) = 7 - 3x and g(x) = 4, what is x?
Answer
(B)
1
46
What is the inverse of f(x) = (x/2) + 3?
Answer
(A)
2x-6
47
What is the range of f(x) = x² if the domain is {-3, -2, -1, 0, 1, 2, 3}?
Answer
(B)
{0, 1, 4, 9}
48
If f(x) = 2x - 3 and g(x) = x+4, calculate g(f(x)).
Answer
(B)
2x+1
49
What do we call the set of values of a function resulting from the input?
Answer
(B)
Range
50
If g(x) = 6 - 2x, which of the following is equivalent to g(3)?
Answer
(A)
3