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# Mathematics Composition of Functions and Invertible Functions Quiz

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### 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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