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Let f: {1, 2, 3} → {1, 2, 3} be an onto function. Then, f is
- a)onto only
- b)one-one and onto
- c)not one one
- d)insufficient information
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Let f: {1, 2, 3} → {1, 2, 3} be an onto function. Then, f is̴...
According to given condition, y=x+c may be the require function, which is also increasing function so one one function
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Let f: {1, 2, 3} → {1, 2, 3} be an onto function. Then, f is̴...
(i) f(1)=1,f(2)=2,f(3)=3
(ii) f(1)=1,f(2)=3,f(3)=2
(iii) f(1)=2,f(2)=3,f(3)=1
(iv) f(1)=2,f(2)=1,f(3)=3
(v) f(1)=3,f(2)=1,f(3)=2
(vi) f(1)=3,f(2)=2,f(3)=1
Since, f is onto, all elements of {1,2,3} have unique pre-image.
The above cases are possible.
Since, every element 1,2,3 has either of image 1,2,3 and that image is unique.
∴ f is one-one.
∴ Function f:A→A is one-one.
(ii) f(1)=1,f(2)=3,f(3)=2
(iii) f(1)=2,f(2)=3,f(3)=1
(iv) f(1)=2,f(2)=1,f(3)=3
(v) f(1)=3,f(2)=1,f(3)=2
(vi) f(1)=3,f(2)=2,f(3)=1
Since, f is onto, all elements of {1,2,3} have unique pre-image.
The above cases are possible.
Since, every element 1,2,3 has either of image 1,2,3 and that image is unique.
∴ f is one-one.
∴ Function f:A→A is one-one.
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Let f: {1, 2, 3} → {1, 2, 3} be an onto function. Then, f isa)onto onlyb)one-one and ontoc)not one oned)insufficient informationCorrect answer is option 'B'. Can you explain this answer?
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