Q. If F = {x, y, z}, what is the size of the power set of F?
Solution
The size of the power set is 2^n where n is the number of elements in the set. Here, n = 3, so the size is 2^3 = 8.
Correct Answer: C — 8
Learn More →
Q. If F = {x, y}, how many subsets of F are there that do not contain 'y'?
Solution
The subsets of F that do not contain 'y' are {∅, {x}}, totaling 2 subsets.
Correct Answer: A — 1
Learn More →
Q. If f(x) = 1/(x-1), what is the point of discontinuity?
-
A.
x = 0
-
B.
x = 1
-
C.
x = -1
-
D.
x = 2
Solution
The function is discontinuous at x = 1 because it leads to division by zero.
Correct Answer: B — x = 1
Learn More →
Q. If f(x) = 2x + 3, what is f(4)?
Solution
Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.
Correct Answer: B — 11
Learn More →
Q. If f(x) = 2x + 3, what is f(5)?
Solution
f(5) = 2(5) + 3 = 10 + 3 = 13.
Correct Answer: B — 13
Learn More →
Q. If f(x) = 2x^2 - 3x + 1, what is f(2)?
Solution
f(2) = 2(2^2) - 3(2) + 1 = 8 - 6 + 1 = 3.
Correct Answer: C — 5
Learn More →
Q. If f(x) = 2x^3 - 9x^2 + 12x, find the intervals where f(x) is increasing.
-
A.
(-∞, 1)
-
B.
(1, 3)
-
C.
(3, ∞)
-
D.
(0, 2)
Solution
Find f'(x) = 6x^2 - 18x + 12. Setting f'(x) = 0 gives x = 1 and x = 2. Testing intervals, f(x) is increasing on (1, 3).
Correct Answer: B — (1, 3)
Learn More →
Q. If f(x) = 2^x, what is f(3)?
Q. If f(x) = 3x - 4, find f(-2).
Solution
f(-2) = 3(-2) - 4 = -6 - 4 = -10.
Correct Answer: A — -10
Learn More →
Q. If f(x) = 3x - 4, what is f(-2)?
Solution
f(-2) = 3(-2) - 4 = -6 - 4 = -10.
Correct Answer: A — -10
Learn More →
Q. If f(x) = 3x - 4, what is the inverse function f^(-1)(x)?
-
A.
(x + 4)/3
-
B.
3x + 4
-
C.
3(x - 4)
-
D.
x/3 + 4
Solution
To find the inverse, set y = 3x - 4, solve for x: x = (y + 4)/3, thus f^(-1)(x) = (x + 4)/3.
Correct Answer: A — (x + 4)/3
Learn More →
Q. If f(x) = 3x - 5, what is f(f(1))?
Solution
First, find f(1) = 3(1) - 5 = -2. Then, f(-2) = 3(-2) - 5 = -6 - 5 = -11.
Correct Answer: D — 7
Learn More →
Q. If f(x) = 5x^2 + 3x, what is f'(1)?
Solution
f'(x) = 10x + 3; f'(1) = 10*1 + 3 = 13.
Correct Answer: B — 10
Learn More →
Q. If f(x) = e^(2x), what is f'(x)?
-
A.
2e^(2x)
-
B.
e^(2x)
-
C.
2x*e^(2x)
-
D.
e^(x)
Solution
Using the chain rule, f'(x) = 2e^(2x).
Correct Answer: A — 2e^(2x)
Learn More →
Q. If f(x) = e^x - x^2, find the x-coordinate of the local maximum.
Solution
Find f'(x) = e^x - 2x. Setting f'(x) = 0 gives a local maximum at x = 1.
Correct Answer: B — 1
Learn More →
Q. If f(x) = e^x, then f'(0) is equal to?
Solution
f'(x) = e^x; f'(0) = e^0 = 1.
Correct Answer: B — 1
Learn More →
Q. If f(x) = e^x, what is f''(0)?
Solution
f''(x) = e^x, thus f''(0) = e^0 = 1.
Correct Answer: A — 1
Learn More →
Q. If f(x) = ln(x) + x^2, then the function is increasing for:
-
A.
x > 0
-
B.
x < 0
-
C.
x > 1
-
D.
x < 1
Solution
The derivative f'(x) = 1/x + 2x. For f'(x) > 0, we need 1/x + 2x > 0, which holds for x > 0.
Correct Answer: A — x > 0
Learn More →
Q. If f(x) = ln(x) for x > 0, is f differentiable at x = 1?
-
A.
Yes
-
B.
No
-
C.
Only continuous
-
D.
Only left differentiable
Solution
f'(x) = 1/x; f'(1) = 1, hence f is differentiable at x = 1.
Correct Answer: A — Yes
Learn More →
Q. If f(x) = ln(x), what is f'(x)?
-
A.
1/x
-
B.
x
-
C.
ln(x)
-
D.
0
Q. If f(x) = sin(x) + cos(x), then the critical points in the interval [0, 2π] are:
-
A.
π/4, 5π/4
-
B.
π/2, 3π/2
-
C.
0, π
-
D.
π/3, 2π/3
Solution
To find critical points, we set f'(x) = cos(x) - sin(x) = 0. This gives tan(x) = 1, leading to x = π/4 and x = 5π/4 in the interval [0, 2π].
Correct Answer: A — π/4, 5π/4
Learn More →
Q. If f(x) = sin(x), what is f(π/2)?
-
A.
0
-
B.
1
-
C.
-1
-
D.
undefined
Solution
f(π/2) = sin(π/2) = 1.
Correct Answer: B — 1
Learn More →
Q. If f(x) = x^2 + 2x + 1 for x < 0 and f(x) = kx + 1 for x >= 0, find k such that f is differentiable at x = 0.
Solution
Setting the left-hand derivative equal to the right-hand derivative at x = 0 gives k = 2.
Correct Answer: A — -1
Learn More →
Q. If f(x) = x^2 + 2x + 1, find f'(1).
Solution
f'(x) = 2x + 2, thus f'(1) = 2(1) + 2 = 4.
Correct Answer: C — 3
Learn More →
Q. If f(x) = x^2 + 2x + 1, what is f'(1)?
Solution
Calculating the derivative f'(x) = 2x + 2, we find f'(1) = 4.
Correct Answer: B — 3
Learn More →
Q. If f(x) = x^2 + 2x + 1, what is the vertex of the parabola?
-
A.
(-1, 0)
-
B.
(0, 1)
-
C.
(-1, 1)
-
D.
(1, 0)
Solution
The vertex form is f(x) = (x + 1)^2, so the vertex is (-1, 0).
Correct Answer: C — (-1, 1)
Learn More →
Q. If f(x) = x^2 + 2x + 3, find f'(1).
Solution
f'(x) = 2x + 2. Therefore, f'(1) = 2(1) + 2 = 4.
Correct Answer: C — 4
Learn More →
Q. If f(x) = x^2 - 4, what are the x-intercepts?
-
A.
-2, 2
-
B.
0, 4
-
C.
2, 4
-
D.
None
Solution
To find x-intercepts, set f(x) = 0: x^2 - 4 = 0, which gives x = ±2.
Correct Answer: A — -2, 2
Learn More →
Q. If f(x) = x^2 - 4, what is the limit of f(x) as x approaches 2?
-
A.
0
-
B.
2
-
C.
4
-
D.
Undefined
Solution
The limit as x approaches 2 is f(2) = 2^2 - 4 = 0.
Correct Answer: C — 4
Learn More →
Q. If f(x) = x^2 - 4x + 3, what is the value of f(2)?
Solution
f(2) = 2^2 - 4*2 + 3 = 4 - 8 + 3 = -1.
Correct Answer: A — 0
Learn More →
Showing 1201 to 1230 of 2847 (95 Pages)
