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Consider the identity function IN : N...

Consider the identity function `I_N : N->N` defined as, `I_N(x)=x` for all `x in N` . Show that although `I_N` is onto but `I_N+I_N : N->N` defined as `(I_N+I_N)(x)=I_N(x)+I_N(x)=x+x=2x` is not onto.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let f: N-{1}->N be defined by, f(n)= the highest prime factor of n ...

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  2. Let A={1,2} . Find all one-to-one function from A to A.

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  3. Consider the identity function IN : N->N defined as, IN(x)=x for al...

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  4. Consider a function f:[0,pi/2]->R given by f(x)=sin x and g:[0,pi/2]->...

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  5. Let f:X->Y be a function. Define a relation R in X given by R={(a,b):f...

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  6. Show that the function f: R->{x in R :-1ltxlt1} defined by f(x)=x/(1+...

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  7. Show that the function f: R->R given by f(x)=x^3+x is a bijection.

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  8. check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if ...

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  9. Show that the function f: N->N given by, f(n)=n-(-1)^n for all n in N...

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  10. Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1...

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  11. Let A be a finite set. If f: A->A is a one-one function, show that ...

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  12. Let A be a finite set. If f: A->A is an onto function, show that f ...

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  13. Give an example of a function which is one-one but not onto. whi...

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  14. Which of the following functions from A to B are one-one and onto? ...

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  15. Prove that the function f: N->N , defined by f(x)=x^2+x+1 is one-on...

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  16. Let A={-1,\ 0,\ 1} and f={(x ,\ x^2): x in A} . Show that f: A->A is ...

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  17. Classify f: N->N given by f(x)=x^2 as injection, surjection or bije...

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  18. Classify f: Z->Z given by f(x)=x^2 as injection, surjection or bije...

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  19. Classify f: N->N given by f(x)=x^3 as injection, surjection or bije...

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  20. Classify f: Z->Z given by f(x)=x^3 as injection, surjection or bije...

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