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Mathematics for IGCSE & O level - Functions (Section 3)

1
For the function h(x) = x^2 + 3, what is h(-4)?
Answer
(B)
13
2
If g(x) = 3x + 5 and h(x) = x^2, what is (g(h(x))?
Answer
(A)
3x^2 + 5
3
When h(x) = x^2/5, find h(2).
Answer
(A)
0.6
4
If g(x) = 7 - 3x, what is g(2)?
Answer
(A)
1
5
If f(x)=x^2 and g(x) = x+1, what is g(f(x))?
Answer
(A)
x^2+1
6
Which of the following represents the domain of a function?
Answer
(A)
The set of starting values of x
7
If f(x) = x^2 + 3 and x = -1, which of the following represents f(x)?
Answer
(B)
2
8
If f(x) = 3x-5, what is the value of x when f(x) = 10?
Answer
(C)
5
9
For the function g(x) = (1/x) - 1/x, find g(12).
Answer
(B)
-1/12
10
If f(x) = 1/x, what are the restrictions on x for the function?
Answer
(C)
x ≠ 0
11
What is the range of the function g(x)=x² if the domain is {-2,-1,0,1,2}?
Answer
(B)
{0, 1, 4}
12
If g(x) = x/4, what is g(8)?
Answer
(B)
2
13
If g(x) = x/4, and x=16, what is g(x)?
Answer
(B)
4
14
If f(x) = 2x + 1 and g(x) = 3x - 2, what is g(f(x))?
Answer
(A)
6x - 1
15
If g(x) = 7 - 3x, and g(x) = 1, what is x?
Answer
(B)
-2
16
Find the inverse of f(x) = x/3 - 1
Answer
(A)
3x+1
17
If f(x) = 3x - 5 and f⁻¹(x) = (x+5)/3, which statement is correct?
Answer
A
B
C
18
What does g(f(x)) represent in composite functions?
Answer
(B)
First finding f(x), then g(x)
19
Given g(x) = (2x+1)/3 and h(x) = 4x - 1, find g(h(x)).
Answer
(A)
(8x+1)/3
20
If f(x) = 3(2x-5) and x=5, what is f(x)?
Answer
(B)
15
21
Which statement is true about the relationship between a function, f(x), and its inverse, f⁻¹(x)?
Answer
A
B
C
22
If g(x) = x/4, what value of x yields g(x) = 1?
Answer
(C)
4
23
What is the domain restriction for f(x) = 1/(x-2)?
Answer
(B)
x≠2
24
Given f(x) = x + 4e, what is f(2)?
Answer
(A)
2 + 4e
25
If f(x) = x + 4e, what is f(-e)?
Answer
(C)
-3e
26
In the context of functions, what does the notation f: x -> 3x + 1 signify?
Answer
(A)
The function maps x to 3x + 1
27
If f(x) = x^2 + 3, what is f(2)?
Answer
(B)
7
28
Given f(x) = 3x-5 and f(x)=25, what is x?
Answer
(C)
10
29
If f(x) = 1/x, and the domain does not include 0, what is the range of this function?
Answer
(B)
All real numbers except 0
30
What does 'f: x -> 3x + 1' represent?
Answer
(B)
A function that maps x to 3x+1
31
Which expression represents the inverse function of f(x) = 5x + 2?
Answer
(A)
(x-2)/5
32
In the function notation f(x), what does the 'x' represent?
Answer
(A)
The input value
33
If f(x) = 3x-5, what x value satisfies f(x) = -2?
Answer
(A)
1
34
If f(x) = x + 4e, and f(x) = 0, what is the value of x?
Answer
(B)
-4e
35
If f(x) = 2x - 3 and g(x) = x + 4, find f(g(x)).
Answer
(A)
2x+5
36
If g(x) = 3x + 5 and h(x) = x², find h(g(x)).
Answer
(B)
(3x + 5)^2
37
For a function, what does the term 'range' refer to?
Answer
(B)
The set of all possible output values
38
What does the function f(x) = 3x + 1 mean?
Answer
B
C
D
39
What is the inverse of the function f(x) = x/4?
Answer
(A)
f⁻¹(x) = 4x
40
If g(x) = 6 - 2x, and g(x) = 2, what is x?
Answer
(B)
2
41
If f(x) = 6 - 2x, what is f(2)?
Answer
(B)
2
42
Which of the following are true about the range of a function?
Answer
B
C
43
If f(x) = 5x - 5, what is the inverse function, f⁻¹(x) equal to?
Answer
(B)
(x + 5) / 5
44
If f(x) = 3x-5, find the x value when f(x)=7.
Answer
(B)
2
45
Given f(x) = x + 5, and the inverse of the function f⁻¹(x) = x-5, find f⁻¹(10).
Answer
(B)
15
46
If f(x) = 1/x, which x values are invalid?
Answer
(C)
x = 0
47
What is the purpose of a mapping diagram?
Answer
(B)
To represent the effect of a function on a given domain
48
If f(x) = 2x + 1 and g(x) = x - 3, what is f(g(x))?
Answer
(A)
2x - 5
49
What is the inverse of f(x) = 2x- 2?
Answer
(B)
(x+2)/2
50
If f(x)=2x-1, what is f⁻¹(x)?
Answer
(A)
(x+1)/2