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Let f: ZrarrZ be defined by f(n)=3n for ...

Let `f: ZrarrZ` be defined by `f(n)=3n` for all `n in Z` and `g: ZrarrZ` be defined by `g(n)={(n/3,if n "is a m u l ti pl e of" 3),(0,if n "i s no t m u l t i p l e of" 3):}` for all `n in Z` Show that `gof=I_Z` and `fog!=I_Z`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A={1,2,..., n} and B={a , b }. Then number of surjections from A...

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  2. If f: Rvec (-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x...

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  3. Let f: ZrarrZ be defined by f(n)=3n for all n in Z and g: ZrarrZ be d...

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  4. Let A={x in R :0lt=xlt=1}dot If f: A->A is defined by f(x)={(x ,, if ...

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  5. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

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  6. Let R be a relation on the set A of ordered pairs of positive intege...

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  7. Let A be a finite set. If f: AvecA is an onto function, show that f is...

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

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

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

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

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

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

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

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

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

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

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

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

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