Injection, Surjection, Bijection and Types of Functions

An injective function is also known as:

• One-to-one function

• Many-to-one function

• Onto function

• None of the above

A function f: A → B is surjective if:

• For every a ∈ A, there exists b ∈ B such that f(a) = b

• For every b ∈ B, there exists a ∈ A such that f(a) = b

• There exists a function g: B → A such that g(f(a)) = a for all a ∈ A

• None of the above

If a function is both injective and surjective, it is called:

• An injective function

• A surjective function

• A bijection

• None of the above

A function f: A → B is injective if and only if:

• Every element of B is mapped to exactly one element of A

• No two elements of B are mapped to the same element of A

• Every element of A is mapped to exactly one element of B

• Both A and B are true

Which of the following is an example of a surjective function?

• f(x) = x^2

• f(x) = 2x

• f(x) = sin(x)

• None of the above

Which of the following is a necessary condition for a function to be a bijection?

• It must be surjective

• It must be injective

• It must be both surjective and injective

• None of the above

A function that can be written in the form f(x) = mx + b is a:

• Polynomial function

• Trigonometric function

• Linear function

• Rational function

A function that involves powers of x is a Polynomial function

• True

• False

A function that involves exponential functions is a:

• Exponential function

• Trigonometric function

What is the greatest integer function of 3.2?

• 3

• 4

• 2

• 3.2