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Let f: N-[1]vecN be defined by, f(n)= th...

Let `f: N-[1]vecN` be defined by, `f(n)=` the highest prime factor of`n` . Show that `f` is neither one-one nor onto. Find the range of `fdot`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Show that the function f: Rvec R given by f(x)=x^3+x is a bijection.

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

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  3. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

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

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  5. Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show tha...

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  6. Verify assoiativity for the following three mappings : f: N->Z0 (t...

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  7. If the set A contains 5 elements and the set B contains 6 elements, th...

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  8. If the set A contains 7 elements and the set B contains 10 elements, ...

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  9. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

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  10. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

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  11. Let A={1,2,3}dot Write all one-one from A to itself.

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  12. If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a b...

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  13. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

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  14. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

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  15. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

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  16. Show that the function f: R ->R is given by f(x)=1+x^2 is not invertib...

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  17. int0^(pi/2)frac{2^sinx}{2^sinx+2^cosx}dx

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  18. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

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  19. Let f: NvecR be a function defined as f(x)=4x^2+12 x+15. Show that f: ...

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  20. Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f...

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