doubt in maths mock test

[Maebara keiichi]

in question 5, option 5 how is the function surjective?

[Kaushal Patil]

Hi

In the option 5, we are getting output same as the input as f(n)=n. The given Domain of the function is R which will also become the Range of the function. So Range of the function is R. Thus Range and Co-Domain are the same.

Hope it helps.

[Maebara keiichi]

but a function is surjective if more than one value give the same output

[Kaushal Patil]

Surjective means Onto which shows that range of the function is same as its Co Domain. 

What you are talking about is the many one function and it does not have a specific name.

Surjective means when Range of Function is same as its Co Domain and 

Injective means when every input has only one output and each output has unique input.   

[akshay]

in simple words ..

1 - if a function is defined for every x € R then it is SURJECTIVE 

2 - if one x gives one y then injective ..

note - One to many is not defined ...

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[Maebara keiichi]

exactly, so how come option 5 is surjective?

[subhajit POD]

No,  If a function give same output for two different inputs then the function is not injective, that has nothing to do with surjectivity.  If the range of the function is same as the codomain of the function then the function is surjective. 

Now try this for option 5. Hope it will clarify your doubt. 

Best

Subhajit

[Maebara keiichi]

yeah i understood it now, i got the answer, thank you

[Bala Suryanarayana Murthy Kotamarthy]

Same for mock Q 5-Can someone please help.

I understood op.5 is surjective as -1.domain=codomain- N.

-2.f(n)= n so every element in domain is mapping to an element in codomain

-so it's I can say injective, surjective & bijective.i.e., it's actually equivalence..

Now op.4..0 in codomain is left out as for no n,f(n) equals 0. So it should not be surjective.

Op.1, only 0,1 values in range so definitely not a surjection , no injection either.

Op.2( like 4 acc. to me) ..0 is left out.f(0)=1 and no n maps to 0.

Op 3. 2 is left out 

This was my approach.

Please let me know what I am missing and what was you guys' approach.

Thank you.

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