[
  {
    "Question": "What is the inverse of the function f(x) = 2x + 3?",
    "Answer": "B",
    "Explanation": "To find the inverse, we switch x and y and solve for y. Starting with y = 2x + 3, we get x = 2y + 3, leading to y = (x - 3)/2. Thus, the inverse is f⁻¹(x) = (x - 3)/2.",
    "PictureURL": "",
    "OptionA": "f⁻¹(x) = 2x - 3",
    "OptionB": "f⁻¹(x) = (x - 3)/2",
    "OptionC": "f⁻¹(x) = 2(x + 3)",
    "OptionD": "f⁻¹(x) = x/2 - 3",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse Functions",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "inverse-functions/one-to-one"
  },
  {
    "Question": "Which of the following functions is one-to-one?",
    "Answer": "A",
    "Explanation": "A function is one-to-one if it passes the horizontal line test. The function f(x) = x^2 is not one-to-one because horizontal lines can intersect it at two points, while f(x) = x is one-to-one.",
    "PictureURL": "https://upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Horizontal_line_test.svg/1200px-Horizontal_line_test.svg.png",
    "OptionA": "f(x) = x",
    "OptionB": "f(x) = x^2",
    "OptionC": "f(x) = sin(x)",
    "OptionD": "f(x) = e^x",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "One-to-One Functions",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "inverse-functions/one-to-one"
  },
  {
    "Question": "What is the inverse of the function f(x) = sin(x)?",
    "Answer": "C",
    "Explanation": "The inverse of the sine function is the arcsine function, denoted as sin⁻¹(x) or arcsin(x). This function gives the angle whose sine is x.",
    "PictureURL": "",
    "OptionA": "cos(x)",
    "OptionB": "tan(x)",
    "OptionC": "arcsin(x)",
    "OptionD": "sec(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Trigonometric Functions",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "inverse-functions/trig-inverses"
  },
  {
    "Question": "If f(x) = e^x, what is f⁻¹(x)?",
    "Answer": "D",
    "Explanation": "The inverse of the exponential function f(x) = e^x is the natural logarithm function, denoted as ln(x). Thus, f⁻¹(x) = ln(x).",
    "PictureURL": "",
    "OptionA": "log(x)",
    "OptionB": "e^x",
    "OptionC": "x^e",
    "OptionD": "ln(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Exponential Functions",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "inverse-functions/exponential-inverses"
  },
  {
    "Question": "What is the range of the function f(x) = ln(x)?",
    "Answer": "B",
    "Explanation": "The natural logarithm function ln(x) is defined for x > 0 and its range is all real numbers (-∞, ∞).",
    "PictureURL": "",
    "OptionA": "(0, ∞)",
    "OptionB": "(-∞, ∞)",
    "OptionC": "(−1, 1)",
    "OptionD": "(−∞, 0)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Range of Logarithmic Functions",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "inverse-functions/logarithmic"
  },
  {
    "Question": "Which of the following is the correct domain for the function f(x) = log(x)?",
    "Answer": "C",
    "Explanation": "The logarithmic function log(x) is defined only for positive values of x, so its domain is (0, ∞).",
    "PictureURL": "",
    "OptionA": "(-∞, 0)",
    "OptionB": "(0, 1)",
    "OptionC": "(0, ∞)",
    "OptionD": "(-∞, ∞)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Domain of Logarithmic Functions",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "inverse-functions/logarithmic"
  },
  {
    "Question": "What is the inverse of the function f(x) = cos(x)?",
    "Answer": "A",
    "Explanation": "The inverse of the cosine function is the arccosine function, denoted as cos⁻¹(x) or arccos(x). This function gives the angle whose cosine is x.",
    "PictureURL": "",
    "OptionA": "arccos(x)",
    "OptionB": "sin(x)",
    "OptionC": "tan(x)",
    "OptionD": "sec(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Trigonometric Functions",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "inverse-functions/trig-inverses"
  },
  {
    "Question": "Which of the following statements is true about one-to-one functions?",
    "Answer": "D",
    "Explanation": "A function is one-to-one if it never takes the same value twice, meaning for every y there is exactly one x. This is crucial for a function to have an inverse.",
    "PictureURL": "",
    "OptionA": "They can have multiple outputs for one input.",
    "OptionB": "They can be defined for all real numbers.",
    "OptionC": "They must be linear functions.",
    "OptionD": "They pass the horizontal line test.",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Properties of One-to-One Functions",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "inverse-functions/one-to-one"
  },
  {
    "Question": "What is the inverse of the function f(x) = 3^x?",
    "Answer": "C",
    "Explanation": "The inverse of the exponential function f(x) = 3^x is the logarithmic function with base 3, denoted as log₃(x). Thus, f⁻¹(x) = log₃(x).",
    "PictureURL": "",
    "OptionA": "ln(x)",
    "OptionB": "log(x)",
    "OptionC": "log₃(x)",
    "OptionD": "3^x",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Exponential Functions",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "inverse-functions/exponential-inverses"
  },
  {
    "Question": "Which of the following functions is not one-to-one?",
    "Answer": "B",
    "Explanation": "The function f(x) = x^2 is not one-to-one because it fails the horizontal line test; horizontal lines can intersect it at two points.",
    "PictureURL": "",
    "OptionA": "f(x) = x + 1",
    "OptionB": "f(x) = x^2",
    "OptionC": "f(x) = e^x",
    "OptionD": "f(x) = ln(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Identifying One-to-One Functions",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "inverse-functions/one-to-one"
  },
  {
    "Question": "What is the range of the function f(x) = sin(x)?",
    "Answer": "A",
    "Explanation": "The sine function oscillates between -1 and 1, so its range is [-1, 1].",
    "PictureURL": "",
    "OptionA": "[-1, 1]",
    "OptionB": "(0, 1)",
    "OptionC": "(-∞, ∞)",
    "OptionD": "[0, 1]",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Range of Trigonometric Functions",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "inverse-functions/trig-inverses"
  },
  {
    "Question": "If f(x) = x^3, what is f⁻¹(x)?",
    "Answer": "B",
    "Explanation": "To find the inverse, we switch x and y and solve for y. Starting with y = x^3, we get x = y^3, leading to y = x^(1/3). Thus, the inverse is f⁻¹(x) = x^(1/3).",
    "PictureURL": "",
    "OptionA": "x^2",
    "OptionB": "x^(1/3)",
    "OptionC": "3^x",
    "OptionD": "x^3 + 1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Polynomial Functions",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "inverse-functions/polynomial-inverses"
  },
  {
    "Question": "What is the inverse of the function f(x) = tan(x)?",
    "Answer": "C",
    "Explanation": "The inverse of the tangent function is the arctangent function, denoted as tan⁻¹(x) or arctan(x). This function gives the angle whose tangent is x.",
    "PictureURL": "",
    "OptionA": "sec(x)",
    "OptionB": "cot(x)",
    "OptionC": "arctan(x)",
    "OptionD": "sin(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Trigonometric Functions",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "inverse-functions/trig-inverses"
  },
  {
    "Question": "Which of the following is true about the inverse of a function?",
    "Answer": "D",
    "Explanation": "The graph of the inverse of a function is a reflection of the original function's graph across the line y = x. This property helps visualize the relationship between a function and its inverse.",
    "PictureURL": "",
    "OptionA": "It is always a linear function.",
    "OptionB": "It has the same domain as the original function.",
    "OptionC": "It is always increasing.",
    "OptionD": "It is a reflection across y = x.",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Properties of Inverses",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "inverse-functions/properties"
  },
  {
    "Question": "What is the inverse of the function f(x) = log₄(x)?",
    "Answer": "B",
    "Explanation": "The inverse of the logarithmic function with base 4 is the exponential function with base 4. Thus, f⁻¹(x) = 4^x.",
    "PictureURL": "",
    "OptionA": "ln(x)",
    "OptionB": "4^x",
    "OptionC": "log(x)",
    "OptionD": "log₄(x)",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Inverse Functions Practice Test",
    "Content Type": "Mathematics",
    "Title": "Inverse of Logarithmic Functions",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "inverse-functions/logarithmic"
  }
]