Q. What is the inverse of the function f(x) = 2x + 5?
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A.
f^-1(x) = (x - 5)/2
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B.
f^-1(x) = 2x - 5
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C.
f^-1(x) = (x + 5)/2
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D.
f^-1(x) = 5 - 2x
Solution
To find the inverse, set y = 2x + 5, solve for x: x = (y - 5)/2, thus f^-1(x) = (x - 5)/2.
Correct Answer: A — f^-1(x) = (x - 5)/2
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Q. What is the inverse of the function f(x) = 3x + 1?
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A.
(x-1)/3
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B.
(x-1)/3
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C.
(x-3)/1
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D.
3(x-1)
Solution
To find the inverse, set y = 3x + 1, solve for x: x = (y - 1)/3.
Correct Answer: A — (x-1)/3
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Q. What is the inverse of the function f(x) = 3x + 4?
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A.
(x - 4)/3
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B.
(x + 4)/3
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C.
3/x - 4
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D.
3/x + 4
Solution
To find the inverse, set y = 3x + 4, solve for x: x = (y - 4)/3, hence the inverse is (x - 4)/3.
Correct Answer: A — (x - 4)/3
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Q. What is the inverse of the function f(x) = 3x - 5?
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A.
(x + 5)/3
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B.
(x - 5)/3
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C.
3(x + 5)
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D.
3(x - 5)
Solution
To find the inverse, set y = 3x - 5, solve for x: x = (y + 5)/3, hence f^(-1)(x) = (x + 5)/3.
Correct Answer: A — (x + 5)/3
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Q. What is the range of the function f(x) = -x^2 + 4?
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A.
(-∞, 4]
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B.
[0, 4]
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C.
[4, ∞)
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D.
(-∞, 0)
Solution
The function is a downward-opening parabola with a maximum value of 4, so the range is (-∞, 4].
Correct Answer: A — (-∞, 4]
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Q. What is the range of the function f(x) = x^2?
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A.
(-∞, ∞)
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B.
[0, ∞)
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C.
(-∞, 0)
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D.
[0, 1]
Solution
The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).
Correct Answer: B — [0, ∞)
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Q. What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?
Solution
The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation f(x) = x^2 - 5x + 6?
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the sum of the roots of the quadratic equation x^2 - 5x + 6 = 0?
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
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Q. What is the value of f(2) if f(x) = x^2 - 2x + 1?
Solution
f(2) = 2^2 - 2(2) + 1 = 4 - 4 + 1 = 1.
Correct Answer: A — 1
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Q. What is the value of k if f(x) = kx^2 + 2x + 1 has a minimum value of -3?
Solution
The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.
Correct Answer: B — -2
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Q. Which of the following functions is an even function?
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A.
f(x) = x^3
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B.
f(x) = x^2
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C.
f(x) = x + 1
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D.
f(x) = sin(x)
Solution
An even function satisfies f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer: B — f(x) = x^2
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Q. Which of the following functions is even?
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A.
f(x) = x^3
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B.
f(x) = x^2
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C.
f(x) = x + 1
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D.
f(x) = sin(x)
Solution
A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.
Correct Answer: B — f(x) = x^2
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Q. Which of the following functions is not a polynomial function?
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A.
f(x) = x^2 + 3x + 1
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B.
g(x) = 2x^3 - 4
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C.
h(x) = sqrt(x)
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D.
k(x) = 5
Solution
h(x) = sqrt(x) is not a polynomial function.
Correct Answer: C — h(x) = sqrt(x)
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Q. Which of the following functions is not a polynomial?
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A.
f(x) = x^3 + 2x^2 - 5
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B.
g(x) = 1/x
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C.
h(x) = 4x - 7
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D.
k(x) = 2
Solution
g(x) = 1/x is not a polynomial because it has a negative exponent.
Correct Answer: B — g(x) = 1/x
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Q. Which of the following functions is not continuous?
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A.
f(x) = x^2
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B.
f(x) = 1/x
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C.
f(x) = sin(x)
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D.
f(x) = e^x
Solution
f(x) = 1/x is not continuous at x = 0.
Correct Answer: B — f(x) = 1/x
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Q. Which of the following functions is periodic?
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A.
f(x) = x
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B.
f(x) = cos(x)
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C.
f(x) = e^x
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D.
f(x) = ln(x)
Solution
The cosine function is periodic with a period of 2π.
Correct Answer: B — f(x) = cos(x)
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Q. Which of the following is a one-to-one function?
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A.
f(x) = x^2
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B.
f(x) = 2x + 3
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C.
f(x) = sin(x)
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D.
f(x) = e^x
Solution
A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.
Correct Answer: B — f(x) = 2x + 3
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Q. Which of the following is an even function?
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A.
f(x) = x^3
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B.
f(x) = x^2
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C.
f(x) = sin(x)
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D.
f(x) = tan(x)
Solution
An even function satisfies f(x) = f(-x). f(x) = x^2 is even.
Correct Answer: B — f(x) = x^2
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Q. Which of the following is the range of the function f(x) = x^2 - 4?
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A.
(-∞, -4]
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B.
[-4, ∞)
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C.
(-4, ∞)
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D.
[0, ∞)
Solution
The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).
Correct Answer: B — [-4, ∞)
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Q. Which of the following is the range of the function f(x) = x^2?
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A.
All real numbers
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B.
All positive real numbers
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C.
All non-negative real numbers
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D.
All integers
Solution
The function f(x) = x^2 is non-negative for all real x, hence the range is all non-negative real numbers.
Correct Answer: C — All non-negative real numbers
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Q. Which of the following is the range of the function f(x) = |x - 1|?
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A.
(-∞, 1)
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B.
[0, ∞)
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C.
(-1, 1)
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D.
[1, ∞)
Solution
The minimum value of |x - 1| is 0 when x = 1, so the range is [0, ∞).
Correct Answer: B — [0, ∞)
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