InterviewSolution
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InterviewSolution
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Defineeach of thefollowing: "(i)injective function """"(ii) surjectivefunction " "(iii) bijective function """"(iv) many -onefunction" "(v) intofunction """ Give anexampleof each typeof functions. |
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Answer» SOLUTION : (i) `f : N to N : f (x) =2x` isinjectivefunctionas ` f(x_(1))=f(x_(2))rArr 2x_(1)=2x_(2)rArr x_(1) = x_(2)` (ii)`A ={1, -1, 2,3}" and"= { 1, 4,9}` Then`f : A toB : f(x) = x^(2)` is surjectivesince eachelementof Bhas atleastonepre -imagein A. (III) Let E be theset of all evennaturalnumbers Then`f N to E : f(x) =2x` is one-oneand ONTO . f is one-onesince `f (x_(1)) = f(x_(2))rArr2x_(1) = 2x_(2) rArr x_(1) =x_(2)` f is ontosince foreach`y in E` thereexists` (1)/(2) y in N ` such that ` f ((1)/(2)y) =y` (iv)Examplegiven in (ii)is many -one . (v)Let `A = {1,2,3} " and" B = {1,4,9,16}` Then `f : A toB : f (x) = x^(2)` is anintofunction sincerange(f) = `{1,4,9 } sub B` |
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