Real-valued functions and algebra of functions - One Line Questions
1.
What is the domain of the function f(x) = sqrt(x^2 - 4)? —
(-inf, -2] U [2, inf)
2.
What is the domain of f(x) = sqrt(x^2 - 9)? —
(-inf, -3] U [3, inf)
3.
A function f is defined by f(x) = sqrt(1-x^2). What is its domain? —
[-1, 1]
4.
A function f is defined by f(x) = sqrt(1-x^2). What is its range? —
[0, 1]
5.
Let f(x) = sqrt(4-x^2). What is the domain of f? —
[-2, 2]
6.
Let f(x) = sqrt(4-x^2). What is the range of f? —
[0, 2]
7.
What is the domain of f(x) = arcsin(x)? —
[-1, 1]
8.
What is the domain of f(x) = 1/sqrt(x-2)? —
(2, inf)
9.
If f(x) = 2x and g(x) = x + 3, what is (f/g)(x)? —
2x/(x+3)
10.
If f(x) = x - 1 and g(x) = x^2, what is (f*g)(x)? —
(x-1)x^2
11.
If f(x) = x^2 and g(x) = x+1, what is (g o f)(x)? —
x^2+1
12.
If f(x) = 3x - 2, what is f^-1(x)? —
(x+2)/3
13.
What is the range of f(x) = sin(x)? —
[-1, 1]
14.
What is the range of the function f(x) = x^2 + 1? —
[1, inf)
15.
What is the range of f(x) = -x^2? —
(-inf, 0]
16.
What is the range of f(x) = arccos(x)? —
[0, pi]
17.
If f(x) = x^2 and g(x) = x^2, what is (f-g)(x)? —
0
18.
Let f(x) = x^2 + 1. Which of the following is NOT in the range of f? —
0
19.
If f(x) = x + 1 and g(x) = 2x, what is (f+g)(x)? —
3x + 1
20.
If f(x) = 2 and g(x) = 3, what is (f+g)(x)? —
5
21.
If f(x) = c (a constant function), what is its domain? —
All real numbers
22.
What is the range of f(x) = log_a(x) where a > 0 and a != 1? —
All real numbers
23.
What is the domain of f(x) = 1/x? —
All real numbers except 0
24.
What is the range of f(x) = |x|? —
All non-negative real numbers
25.
What is the domain of f(x) = ln(x)? —
All positive real numbers
26.
What is the range of f(x) = e^x? —
All positive real numbers
27.
If f(x) = sqrt(x) and g(x) = x^2, what is the domain of (f o g)(x)? —
All real numbers
28.
If f(x) = x^2 and g(x) = sqrt(x), what is the domain of (g o f)(x)? —
All real numbers
29.
What is the domain of f(x) = tan(x)? —
All real numbers except (n + 1/2)*pi, where n is an integer
30.
If f(x) = c (a constant function), what is its range? —
The set {c}
31.
If f(x) = x+1 and g(x) = 1/(x+1), what is the domain of (f*g)(x)? —
All real numbers except -1
32.
If f(x) = x^2 and g(x) = x-1, what is the domain of (f/g)(x)? —
All real numbers except 1
33.
If f(x) = x^2 - 1 and g(x) = x+1, what is the domain of (f/g)(x)? —
All real numbers except -1
34.
What is the range of f(x) = 2^x? —
(0, inf)
35.
If f(x) = sqrt(x-a) and g(x) = x^2, what is the domain of (f o g)(x)? —
All real numbers such that x^2 >= a
36.
If f(x) = x^2 and g(x) = sqrt(x-a), what is the domain of (g o f)(x)? —
All real numbers such that x^2 >= a
37.
What is the domain of f(x) = log_a(x) where a > 0 and a != 1? —
All positive real numbers
38.
If f(x) = x and g(x) = x, then (f/g)(x) is defined for: —
All non-zero real numbers
39.
If f(x) = 0, what is its range? —
The set {0}
40.
If f(x) = x^2 and g(x) = 1/x, what is the domain of (g o f)(x)? —
All real numbers except 0
41.
If f(x) = 1/x and g(x) = x^2, what is the domain of (g o f)(x)? —
All real numbers except 0
42.
If f(x) = x+1 and g(x) = x-1, what is the domain of (f/g)(x)? —
All real numbers except 1
43.
If f(x) = x-1 and g(x) = x+1, what is the domain of (f/g)(x)? —
All real numbers except 1
44.
If f(x) = x and g(x) = c (constant), what is (f+g)(x)? —
x+c
45.
Which of the following is NOT a real-valued function? —
f(x) = sqrt(-x)
46.
If f(x) = x and g(x) = x, then (f-g)(x) is: —
0
47.
If f(x) = x-1 and g(x) = x+1, what is (f o g)(x)? —
x
48.
If f(x) = x+1 and g(x) = x-1, what is (g o f)(x)? —
x
49.
If f(x) = x and g(x) = x, what is (f o g)(x)? —
x
50.
If f(x) = x^3, what is f^-1(x)? —
x^(1/3)