Question

check whether the following functions one to one and onto X={1,2,3,4,} Y={a} and f ={(1,a)(2,a)(3,a)(4,a)}​

Answer 1

13-Jun-2020 — check-circle. Text Solution. A. an one-to-one function. B. an onto function. C. a function which is not one-to-one. D. not a function.

2 answers

 

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Top answer:  

an one-to-one function an onto function a function which is not one-to-one not a function Answer: D

Answer 2

Given :

f ={(1,a)(2,a)(3,a)(4,a)}​

X={1,2,3,4,} Y={a}

one−one:

⇒f (1)=a  

⇒f (2)=a  

⇒f (3)=a  

⇒f (4)=a

Every element of X has different images in Y

∴  Function f is one-one.

Co-domain of f={a,a,a,a,}

Range of f   = set of images {a,a,a,a,}

⇒  Co-domain = range.

∴  Function f  is onto.