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Show that the function f: Rvec R given b...

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

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A be a finite set. If f: AvecA is an onto function, show that f is...

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  2. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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