Podcast
Questions and Answers
Which property ensures that a function is invertible?
Which property ensures that a function is invertible?
- Being one-one and onto (correct)
- Reflexivity
- Symmetry
- Being continuous
What is the definition of an invertible function?
What is the definition of an invertible function?
- A function with a unique value for each input
- A function that is reflexive and symmetric
- A function that is one-one and onto (correct)
- A function that is continuous and increasing
In the context of functions, what does the term 'inverse' refer to?
In the context of functions, what does the term 'inverse' refer to?
- A transformation of the original function
- The opposite direction of the function
- A function that undoes the original function (correct)
- The reciprocal of the function
Why is it beneficial to prove a function is one-one and onto when determining its invertibility?
Why is it beneficial to prove a function is one-one and onto when determining its invertibility?
If a function f : X → Y is invertible, what can be concluded about f?
If a function f : X → Y is invertible, what can be concluded about f?
How can proving a function to be one-one and onto help establish its invertibility?
How can proving a function to be one-one and onto help establish its invertibility?
For the function f(x) = x^4, is f one-one and onto?
For the function f(x) = x^4, is f one-one and onto?
For the function f(x) = 3x, is f one-one and onto?
For the function f(x) = 3x, is f one-one and onto?
If f : A → B and g : B → C are functions, what does the composition gof represent?
If f : A → B and g : B → C are functions, what does the composition gof represent?
In the context of functions, what does it mean for a function to be 'many-one'?
In the context of functions, what does it mean for a function to be 'many-one'?
What does it mean for a function to be 'onto'?
What does it mean for a function to be 'onto'?
When proving invertibility of a function, what property must the function satisfy?
When proving invertibility of a function, what property must the function satisfy?
What is the defining characteristic of a one-one function?
What is the defining characteristic of a one-one function?
Which of the following functions is NOT one-one based on the given information?
Which of the following functions is NOT one-one based on the given information?
What does an onto function ensure according to the text?
What does an onto function ensure according to the text?
Which function from the given figures is onto?
Which function from the given figures is onto?
A function that is both one-one and onto is known as:
A function that is both one-one and onto is known as:
What is the defining characteristic of a many-one function?
What is the defining characteristic of a many-one function?
Flashcards
Invertible Function
Invertible Function
A function that is both one-to-one (or injective) and onto (or surjective).
One-to-one (Injective)
One-to-one (Injective)
A function where each element in the domain maps to a unique element in the codomain.
Onto (Surjective)
Onto (Surjective)
A function where every element in the codomain has at least one corresponding element in the domain.
Many-to-one
Many-to-one
Signup and view all the flashcards
Bijection
Bijection
Signup and view all the flashcards
Inverse Function
Inverse Function
Signup and view all the flashcards
Composition of Functions
Composition of Functions
Signup and view all the flashcards
Function f:X->Y
Function f:X->Y
Signup and view all the flashcards
Codomain
Codomain
Signup and view all the flashcards
Domain
Domain
Signup and view all the flashcards
f(x) = x^4
f(x) = x^4
Signup and view all the flashcards
f(x) = 3x
f(x) = 3x
Signup and view all the flashcards
f2 is not one-one
f2 is not one-one
Signup and view all the flashcards
f4 is onto
f4 is onto
Signup and view all the flashcards
'Onto' function
'Onto' function
Signup and view all the flashcards
gof
gof
Signup and view all the flashcards
'many-one' function
'many-one' function
Signup and view all the flashcards
