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?

Assignment of students to code numbers Signup and view all the answers

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

One-one onto Signup and view all the answers

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

It assigns each student a unique roll number Signup and view all the answers

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

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

Why is R considered an equivalence relation?

Because it satisfies reflexivity, symmetry, and transitivity properties Signup and view all the answers

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

{1 and 3} 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}?

Because elements of {1, 3, 5, 7} are odd while elements of {2, 4, 6} are even 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}?

Two subsets: one with odd numbers and one with even numbers Signup and view all the answers

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

To emphasize the concept of an equivalence relation Signup and view all the answers

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

7 Signup and view all the answers

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

cos(3x^2) Signup and view all the answers

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

Identity function on A Signup and view all the answers

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

Mathematically proven inequality Signup and view all the answers

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

11 Signup and view all the answers

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

11 Signup and view all the answers

What is the main feature of binary operations?

They associate two numbers to produce another number Signup and view all the answers

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

Exponentiation Signup and view all the answers

What does 'binary' refer to in binary operations?

The operation involves two elements at a time Signup and view all the answers

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

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

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

Two Signup and view all the answers

Which of the following statements is true about binary operations?

They can be defined for any set of elements Signup and view all the answers

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

a is related to b under relation R Signup and view all the answers

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

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

What is an empty relation in a set A?

No element of A is related to any other element of A Signup and view all the answers

How would you define a trivial relation?

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

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

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

Which term defines a universal relation?

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