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A function f: X → Y is bijective if and only if
- a)f is one-one only
- b)f is onto only
- c)f is many-one and onto
- d)f is one-one and onto
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A function f: X → Y is bijective if and only ifa)f is one-one onl...
A bijective function is also known as an invertible function. It is a function that has both one-to-one and onto properties.
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A function f: X → Y is bijective if and only ifa)f is one-one onl...
Bijective Functions Explanation:
Bijective functions are functions that are both injective (one-one) and surjective (onto). Let's break down the components of a bijective function:
One-One Function (Injective):
- A function is said to be one-one if each element in the domain maps to a unique element in the codomain.
- In other words, no two different elements in the domain can map to the same element in the codomain.
Onto Function (Surjective):
- A function is said to be onto if every element in the codomain is mapped to by at least one element in the domain.
- In other words, the function covers the entire codomain without leaving any element out.
Bijective Function:
- A function is bijective if it is both one-one and onto.
- This means that every element in the domain maps to a unique element in the codomain, and every element in the codomain is mapped to by at least one element in the domain.
Therefore, the correct option is D - a function is bijective if and only if it is both one-one and onto. This ensures that the function is not only injective but also covers the entire codomain without any gaps or repetitions.
Bijective functions are functions that are both injective (one-one) and surjective (onto). Let's break down the components of a bijective function:
One-One Function (Injective):
- A function is said to be one-one if each element in the domain maps to a unique element in the codomain.
- In other words, no two different elements in the domain can map to the same element in the codomain.
Onto Function (Surjective):
- A function is said to be onto if every element in the codomain is mapped to by at least one element in the domain.
- In other words, the function covers the entire codomain without leaving any element out.
Bijective Function:
- A function is bijective if it is both one-one and onto.
- This means that every element in the domain maps to a unique element in the codomain, and every element in the codomain is mapped to by at least one element in the domain.
Therefore, the correct option is D - a function is bijective if and only if it is both one-one and onto. This ensures that the function is not only injective but also covers the entire codomain without any gaps or repetitions.
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A function f: X → Y is bijective if and only ifa)f is one-one onlyb)f is onto onlyc)f is many-one and ontod)f is one-one and ontoCorrect answer is option 'D'. Can you explain this answer?
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