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Mathematics for IGCSE & O level - Functions (Section 1)

1
If f(x) = 2x-1, then f(g(x)) = 4x+3, find g(x).
Answer
(B)
2x+2
2
If f(x) = 4x - 6, solve for x, given f(x) = 10
Answer
(B)
4
3
If f(x) = 2x - 3, what is the value of f(5)?
Answer
(C)
13
4
If f(x) = 2x + 1, what expression represents f(x+h)?
Answer
(B)
2x + 2h + 1
5
Given the function f(x) = 2x-7, what is the inverse function, f^-1(x) ?
Answer
(A)
(x+7)/2
6
If f(x) = 3x+4, find f^-1(x).
Answer
(A)
(x-4)/3
7
If g(x) = 3x - 1, what is g(4)?
Answer
(C)
12
8
Which of the following is true about the composite function g(f(x))?
Answer
A
B
D
9
The domain of a function includes all possible...
Answer
(B)
Inputs (x-values)
10
What does the notation f^-1(x) represent?
Answer
(B)
The inverse function of f(x)
11
Which of the following could be the domain for f^-1(x), given f(x) has a range of all real numbers?
Answer
(A)
All real numbers
12
If f(x) = 3x + 2, find f(-1).
Answer
(C)
1
13
Which function is represented by this mapping diagram: Domain: {-1, 0, 1, 2} Range: {9, 12, 15, 18}?
Answer
(B)
h(x) = 3x+12
14
Given f(x) = 3x - 5 and g(x) = x + 2, then find f(g(x))
Answer
(A)
3x+1
15
Which of the following is not true about the inverse function?
Answer
(C)
The domain of the inverse function is the same as the domain of the original function.
16
If h(x) = x^2/5, what is h(10)?
Answer
(B)
50
17
If f(x) = x + 3, what is the result of f(x+1)?
Answer
(B)
x+4
18
Given that f(x) = 2x + 1 and g(x) = x^2 - 3, what is f(g(x))?
Answer
(A)
2x^2-5
19
If f(x) = 2x - 5, what is the value of x if f(x) = 3?
Answer
(C)
9/2
20
Given the function f(x) = 2x + 4, find the value of x when f(x) = 0.
Answer
(A)
-2
21
Given the mapping diagram of g(x)=5x+2, where the domain is {-1, 0, 1, 2, 3}, what is g(0)?
Answer
(A)
2
22
If f(x) = 2x + 1 and g(x) = x^2, what is g(f(2))?
Answer
(D)
25
23
What is the domain of the function h(x) = 1/(x-4)?
Answer
(B)
x ≠ 4
24
What is the range of the function g(x)= x^2 with the domain {-2, -1, 0, 1, 2}?
Answer
(B)
{0, 1, 4}
25
If f(x) = 3x - 5, then what is f^-1(7)?
Answer
(C)
16/3
26
If g(x) = x - 2, what is g^-1(x)?
Answer
(A)
x+2
27
Which of the following is true regarding composite functions g(f(x))?
Answer
A
B
D
28
f(x) = x^2. Find f(2) + g(2) if g(x)=x-1
Answer
(D)
7
29
If g(x) = x/4, find g(12).
Answer
(A)
3
30
If f(x) = 2x - 3 and f(x) = 7, what is x?
Answer
(B)
5
31
If f(x) = 3x, then f^-1(x) is:
Answer
(A)
x/3
32
If f(x) = x+2, find f(3).
Answer
(C)
5
33
If f(x)= x/2+1, what is f^-1(x)?
Answer
(A)
2x-2
34
What is the definition of a composite function?
Answer
(C)
A function that operates on the result of another function.
35
Which is the mapping diagram's domain for g(x) = 5x+2 with domain {-1, 0, 1, 2, 3}?
Answer
(B)
{-1, 0, 1, 2, 3}
36
What does g(f(x)) mean?
Answer
(B)
Substitute f(x) into g(x).
37
Given f(x) = x^2 - 4 and g(x) = x+2, find f(g(x)).
Answer
(D)
x^2+4x-4
38
If f(x) = x + 2, then f^-1(x) is:
Answer
(A)
x - 2
39
Which of the following are examples of functions?
Answer
B
C
D
40
The range of a function refers to the set of:
Answer
(B)
Output values
41
If f(x) = x + 5, what is f^-1(x)?
Answer
(A)
x - 5
42
If f(x) = 3x + 1, what is the value of x when f(x) = 10?
Answer
(C)
4
43
Given the functions f(x) = x + 1 and g(x) = x^2, what is g(f(2))?
Answer
(B)
9
44
If f(x) = x + 3, then solve f(x) = 0
Answer
(B)
-3
45
If f(x) = x + 1, what is the result of f(x-1)?
Answer
(A)
x
46
If g(x) = x - 5, what is g(7)?
Answer
(B)
12
47
If f(x) = x^2 -1, then which of the following is equal to f(x+h) - f(x)?
Answer
(A)
2xh+h^2
48
The domain of f(x) = 1/(x-2) is:
Answer
(C)
x≠2
49
What is f(g(x)) if f(x)=x-1 and g(x)=2x?
Answer
(A)
2x-1
50
If f(x)= 3x+1 and g(x)= x-2. Find f(g(3)).
Answer
(B)
7