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Show that f: R->R , defined as f(x)=x^3 ...

Show that `f: R->R` , defined as `f(x)=x^3` , is a bijection.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

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  2. Show that the function f : R ->R, defined as f(x)=x^2, is neither one-...

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  3. Show that f: R->R , defined as f(x)=x^3 , is a bijection.

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  4. Show that the function f: R0->R0 , defined as f(x)=1/x , is one-one on...

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  5. Prove that the greatest integer function f: RR rarr RR, given by f(x)=...

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  6. Show that the modulus function f: R->R , given by f(x)=|x| is neith...

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  7. Let C be the set of complex numbers. Prove that the mapping F:C to R g...

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  8. Show that the function f: Rvec given by f(x)=x a+b , where a , b in R...

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  9. Show that the function f: R->R given by f(x)=cosx for all x in R , is...

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  10. Let A=R-{2} and B=R-{1} . If f: A->B is a mapping defined by f(x)=(...

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  11. Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=...

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  12. Let A be any non-empty set. Then, prove that the identity function on ...

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  13. Let f: N-{1}->N be defined by, f(n)= the highest prime factor of n ...

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

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

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

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

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

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

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

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