Inverse functions and graphs of simple functions - One Line Questions
1.
If f(x) = 2^x, what is its inverse function, f⁻¹(x)? —
log₂(x)
2.
If f(x) = x, what is f⁻¹(x)? —
x
3.
What is the domain of the function f(x) = arcsin(x)? —
[-1, 1]
4.
What is the domain of the inverse function of f(x) = e^x? —
(0, ∞)
5.
What is the domain of the function f(x) = √x? —
[0, ∞)
6.
What is the domain of the function f(x) = log_b(x) where b > 1? —
(0, ∞)
7.
What is the domain of f(x) = cot(x)? —
R - {nπ | n ∈ Z}
8.
What is the domain of the function f(x) = log(x²)? —
R - {0}
9.
What is the domain of f(x) = tan(x)? —
R - {(2n+1)π/2 | n ∈ Z}
10.
What is the domain of f(x) = arcsin(2x)? —
[-1/2, 1/2]
11.
What is the domain of the inverse function of f(x) = log₂(x)? —
(0, ∞)
12.
What is the range of f(x) = sec(x)? —
(-∞, -1] ∪ [1, ∞)
13.
What is the range of f(x) = csc(x)? —
(-∞, -1] ∪ [1, ∞)
14.
What is the principal value range of the inverse trigonometric function arccot(x)? —
(0, π)
15.
What is the principal value range of arccsc(x)? —
(-π/2, π/2) - {0}
16.
What is the range of the function f(x) = arccos(x)? —
[0, π]
17.
The function f(x) = arctan(x) is defined for all real numbers. What is its range? —
(-π/2, π/2)
18.
The range of the function f(x) = sin(x) is: —
[-1, 1]
19.
What is the range of the function f(x) = arcsin(x) + arccos(x)? —
{π/2}
20.
What is the principal value range of arcsec(x)? —
[0, π] - {π/2}
21.
What is the range of f(x) = 3 + arctan(x)? —
(3-π/2, 3+π/2)
22.
What is the value of arccos(0)? —
π/2
23.
What is the value of arctan(1)? —
π/4
24.
What is the value of arccos(-1)? —
π
25.
The graph of y = x² - 1 is a translation of y = x² by: —
1 unit down
26.
If f(x) = 1/x, what is its inverse function, f⁻¹(x)? —
1/x
27.
If f(x) = log_b(x), its inverse function f⁻¹(x) is: —
b^x
28.
The function f(x) = x|x| is: —
Odd
29.
Which function's graph passes through the origin? —
f(x) = x³
30.
Which of the following is NOT an even function? —
f(x) = x³
31.
Which of the following is NOT an odd function? —
f(x) = x²
32.
If f(x) = a^x where a > 0 and a ≠ 1, its inverse function f⁻¹(x) is: —
log_a(x)
33.
The graph of y = 1/(x-a) is a translation of y = 1/x by 'a' units in the: —
Positive x-direction
34.
The graph of y = x³ is symmetric with respect to: —
The origin
35.
The graph of y = x² is symmetric with respect to: —
The y-axis
36.
The graph of y = 1/x² is symmetric with respect to: —
The y-axis
37.
The graph of y = √(-x) is a reflection of the graph of y = √x across: —
The y-axis
38.
The graph of y = -x³ is symmetric with respect to: —
The origin
39.
The graph of y = 1/x is symmetric with respect to: —
The line y = x and the origin
40.
The graph of y = ln(x) is the reflection of y = e^x across: —
The line y = x
41.
The graph of y = x⁴ is flatter than the graph of y = x² near the origin. —
False
42.
The graph of y = c (where c is a constant) is a: —
Horizontal line
43.
If f(x) = x + 1, what is f⁻¹(x)? —
x - 1
44.
The graph of y = |x| has a minimum value at: —
x = 0
45.
The graph of y = tan⁻¹(x) has horizontal asymptotes at: —
y = -π/2 and y = π/2
46.
The graph of y = x^n for odd integer n > 1 is similar to the graph of: —
y = x³
47.
The graph of y = x^n for even integer n > 1 is similar to the graph of: —
y = x²
48.
What is the value of arctan(-√3)? —
-π/3
49.
What is the value of arccot(-1)? —
3π/4
50.
What is the value of arcsin(1/2)? —
π/6