in Set Theory & Algebra
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Given that the function f and g ,  fog is composition of function,

also f and fog is one-to-one functions ,

then what can be said about ?

A) g is one-to-one function

B)can't say anything about g

in Set Theory & Algebra
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2 Comments

A)
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how ?

Can you elaborate?
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1 Answer

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If suppose g is not one-one then for x1!=x2 we have g(x1)=g(x2)=b

 Now as f is one-one f(b)=f(b) -> f(g(x1))=f(g(x2)) with x1!=x2 which contradicts as fog is one one so g should be one one

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how it contradicts fog is one -one ?
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