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Show that the function f: Z->Z defined b...

Show that the function `f: Z->Z` defined by `f(x)=x^2` for all `x in Z` , is a function but not bijective function.

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

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  2. Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

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  3. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

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  4. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

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  5. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

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  6. Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in...

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  7. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

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  8. Show that the Signum function f:R->R, given by f(x)={(1,xgt0),(0,x=0),...

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  9. Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q ...

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  10. Show that the function f: R->R defined by f(x)=3x^3+5 for all x in R ...

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  11. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

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  12. Let A be the set of all 50 students of class X I I in a central scho...

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  13. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

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  14. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

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

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

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

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

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

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

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