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Mathematics Composition of Functions and Invertible Functions Quiz
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Mathematics Composition of Functions and Invertible Functions Quiz

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Questions and Answers

What is the function f(x) = 3x?

  • One-one but not onto (correct)
  • One-one onto
  • Many-one onto
  • Neither one-one nor onto
  • In the given context, what does the function f represent?

  • Roll number assigned to a student (correct)
  • Code number assigned to a roll number
  • Assignment of students to code numbers
  • None of the above
  • What does g(b) = the code number assigned to the roll number b signify?

  • Roll number assigned to a student
  • Code number assigned to a student (correct)
  • Assignment of roll numbers to code numbers
  • None of the above
  • How is the combination of functions f and g defined in this context?

    <p>Assignment of students to code numbers</p> Signup and view all the answers

    What type of function is g : B → C in this scenario?

    <p>One-one onto</p> Signup and view all the answers

    Based on the definitions given, which statement is true about f : A → B?

    <p>It assigns each student a unique roll number</p> Signup and view all the answers

    What is the relation R defined in set A = {1, 2, 3, 4, 5, 6, 7}?

    <p>Pairs of numbers where both are either odd or even</p> Signup and view all the answers

    Why is R considered an equivalence relation?

    <p>Because it satisfies reflexivity, symmetry, and transitivity properties</p> Signup and view all the answers

    Which elements in the subset {1, 3, 5, 7} are related according to the given relation?

    <p>{1 and 3}</p> Signup and view all the answers

    Why are elements in the subset {1, 3, 5, 7} not related to any element in {2, 4, 6}?

    <p>Because elements of {1, 3, 5, 7} are odd while elements of {2, 4, 6} are even</p> Signup and view all the answers

    How many subsets of elements exist in the relation R for the set A = {1, 2, 3, 4, 5, 6, 7}?

    <p>Two subsets: one with odd numbers and one with even numbers</p> Signup and view all the answers

    Why does the relation R include pairs of numbers both being either odd or even?

    <p>To emphasize the concept of an equivalence relation</p> Signup and view all the answers

    What does gof (2) equal to in the given functions f and g?

    <p>7</p> Signup and view all the answers

    If f(x) = cos x and g(x) = 3x^2, what is the value of fog (x)?

    <p>cos(3x^2)</p> Signup and view all the answers

    In the functions given, what is the value of fog?

    <p>Identity function on A</p> Signup and view all the answers

    Why is gof not equal to fog in the provided functions?

    <p>Mathematically proven inequality</p> Signup and view all the answers

    What does gof (5) equal to in the given functions f and g?

    <p>11</p> Signup and view all the answers

    If f(4) = 5 and g(5) = 7, what is the value of gof (4)?

    <p>11</p> Signup and view all the answers

    What is the main feature of binary operations?

    <p>They associate two numbers to produce another number</p> Signup and view all the answers

    Which of the following is NOT a fundamental operation mentioned in the text?

    <p>Exponentiation</p> Signup and view all the answers

    What does 'binary' refer to in binary operations?

    <p>The operation involves two elements at a time</p> Signup and view all the answers

    What is the general definition of a binary operation on a set A?

    <p>A function that combines any pair of elements from A to produce another element in A</p> Signup and view all the answers

    How many numbers can be added or multiplied at a time in binary operations?

    <p>Two</p> Signup and view all the answers

    Which of the following statements is true about binary operations?

    <p>They can be defined for any set of elements</p> Signup and view all the answers

    What do we mean when we say that (a, b) ∈ R?

    <p>a is related to b under relation R</p> Signup and view all the answers

    Which of the following best describes what a universal relation is?

    <p>Each element in a set is related to every other element in the set</p> Signup and view all the answers

    What is an empty relation in a set A?

    <p>No element of A is related to any other element of A</p> Signup and view all the answers

    How would you define a trivial relation?

    <p>A relation where no elements are related to each other</p> Signup and view all the answers

    In the context of relations, what does the notation R = {(a, b): a – b = 10} signify?

    <p>The set of all pairs where the difference between the elements is 10</p> Signup and view all the answers

    Which term defines a universal relation?

    <p>Each element of a set is connected to every other element</p> Signup and view all the answers

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