Understanding Invertibility in Functions

The video tutorial explains the concept of invertibility in functions, detailing the conditions required for a function to be invertible. It covers the necessity of a unique mapping from the domain to the co-domain and introduces the terms 'one-to-one' (injective) and 'onto' (surjective) functions. The tutorial restates the conditions for invertibility using these terms, emphasizing that a function is invertible if it is both injective and surjective.

What is the condition for a function to be considered invertible?

• The function maps every element in the domain to itself.

• The function has no elements in the co-domain.

• For every element in the co-domain, there is a unique element in the domain that maps to it.

• Every element in the domain maps to multiple elements in the co-domain.

What does the identity function imply in the context of invertibility?

• It maps every element to zero.

• It maps every element to itself.

• It maps no elements.

• It maps every element to a different element.

What breaks the condition of invertibility in a function?

• Having a unique mapping for each element in the co-domain.

• Having multiple elements in the domain map to the same element in the co-domain.

• Mapping no elements in the domain.

• Mapping every element in the domain to itself.

What is another term for a one-to-one function?

• Reflective

• Injective

• Bijective

• Surjective

What is required for a function to be surjective?

• Every element in the domain maps to multiple elements in the co-domain.

• No elements in the co-domain are mapped to.

• Every element in the co-domain is mapped to by at least one element in the domain.

• Every element in the domain maps to itself.

What does it mean for a function to be onto?

• It maps every element in the domain to itself.

• It maps every element in the domain to a different element.

• Every element in the co-domain is mapped to by the domain.

• No elements in the co-domain are mapped to.

What is the relationship between surjective and injective functions for invertibility?

• A function must be neither surjective nor injective.

• A function must be surjective but not injective.

• A function must be both surjective and injective.

• A function must be either surjective or injective.

What is the less formal term for an injective function?

• None-to-one

• Many-to-one

• One-to-one

• Onto

What is the less formal term for a surjective function?

• Many-to-one

• One-to-one

• Onto

• None-to-one

What is the condition for a function to be invertible using formal terminology?

• The function is neither surjective nor injective.

• The function is both surjective and injective.

• The function is surjective but not injective.

• The function is injective but not surjective.