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On the set Z of all integers define f ; Z → Z as follows : f (x) = {x/2 if x is even, and f (x) = 0 if x is odd , then f is

  • a)
    onto but not one-one

  • b)
    into

  • c)
    one-one but not onto

  • d)
    one-one and onto

Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
On the set Z of all integers define f ; Z→Z as follows : f (x) = ...
If u take even digits like 2,4,6.....the in the codomain the value are .....-2,-1,1,2,3....... when u take odd digits the value becomes 0 as the codomain satisfy the onto condition. where as coming to one one all even digits have one and only image and odd digits have 0 but every element in domain have one and only image in codomain
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Community Answer
On the set Z of all integers define f ; Z→Z as follows : f (x) = ...
f(x) = {x/2 x is even,     0 x is odd}
f(1) = f(3) = f(5) = f(odd) = 0
Hence f is not one - one. 
column = Z
Range = {0, even}
= {0,2,4,6,8,10.......}
f(x) = x/2 implies even
f(odd) = 0
Range is not equal to codomain 
Hence, onto
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On the set Z of all integers define f ; Z→Z as follows : f (x) = {x/2if x is even, and f (x) = 0 if x is odd , then f isa)onto but not one-oneb)intoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about On the set Z of all integers define f ; Z→Z as follows : f (x) = {x/2if x is even, and f (x) = 0 if x is odd , then f isa)onto but not one-oneb)intoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the set Z of all integers define f ; Z→Z as follows : f (x) = {x/2if x is even, and f (x) = 0 if x is odd , then f isa)onto but not one-oneb)intoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer?.
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