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If f: A→B and g:B→C are onto , then gof:A→C is:
- a)a many-one and onto function
- b)a bijective function
- c)an into function
- d)an onto function
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If f: A→B and g:B→C are onto , then gof:A→C is:̴...
Explanation:
Onto Function:
An onto function is a function where every element in the codomain (set B) is mapped to by at least one element in the domain (set A). In other words, for every element in B, there is at least one element in A that maps to it.
Composition of Functions:
When we compose two functions f: A→B and g: B→C, we create a new function gof: A→C. This new function maps elements from set A to set C by first applying the function f to map elements from A to B, and then applying the function g to map elements from B to C.
Properties of the Composition:
- If both f and g are onto functions, then the composition gof will also be onto.
- The composition gof may not necessarily be many-one or bijective.
Answer:
In this case, since both f and g are onto functions, the composition gof will also be onto. This means that every element in set C will have at least one element in set A that maps to it through the function gof. Therefore, the correct answer is option 'D' - An onto function.
Onto Function:
An onto function is a function where every element in the codomain (set B) is mapped to by at least one element in the domain (set A). In other words, for every element in B, there is at least one element in A that maps to it.
Composition of Functions:
When we compose two functions f: A→B and g: B→C, we create a new function gof: A→C. This new function maps elements from set A to set C by first applying the function f to map elements from A to B, and then applying the function g to map elements from B to C.
Properties of the Composition:
- If both f and g are onto functions, then the composition gof will also be onto.
- The composition gof may not necessarily be many-one or bijective.
Answer:
In this case, since both f and g are onto functions, the composition gof will also be onto. This means that every element in set C will have at least one element in set A that maps to it through the function gof. Therefore, the correct answer is option 'D' - An onto function.
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If f: A→B and g:B→C are onto , then gof:A→C is:a)a many-one and onto functionb)a bijective functionc)an into functiond)an onto functionCorrect answer is option 'D'. Can you explain this answer?
Question Description
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