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Using the definition ,prove that the function F : `AtoB` is invertible if and only if f is both one -one and onto.

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Solutions of NCERT Exemplar Problems (Long Answer Type Questions)
  1. Let A = R - {3} , B = R - {1} . If f : A rarr B be defined f(x) = (x-2...

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  2. Let A = [-1,1] . Then , discuss whether the following functions define...

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  3. Let A = [-1,1] . Then , discuss whether the following functions define...

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  4. Check the injectivity and surjectivity of the following function . f...

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  5. Let A = [-1,1] . Then , discuss whether the following functions define...

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  6. Each of the following defines a relation of N : x is greater than y...

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  7. Each of the following defines a relation of N : x+y = 10 , x , y in ...

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  8. Each of the following defines a relation of N : x. y is square of a...

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  9. Each of the following defines a relation of N : x+4y =10 , x , y in ...

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  10. Let A = {1,2,3.......9} and R be the relation in AxxA defined by (a,b)...

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  11. Using the definition ,prove that the function F : AtoB is invertible ...

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  12. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  13. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  14. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  15. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  16. Let ** be the binary operation defined on Q. Find which of the follow...

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  17. Let ** be the binary operation defined on Q. Find which of the follow...

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  18. Let ** be the binary operation defined on Q. Find which of the follow...

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  19. Let ** be the binary operation defined on Q. Find which of the follow...

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  20. If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R ....

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