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

Let `f: ZvecZ` be defined by `f(n)=3n` for all `n in Z` and `g: Zvec` be defined by `f(n)={n/3,ifni samul t i p l eof3 0,ifni snotmul t i p l eof3fora l ln in Zdot` Show that `gof=I_Z` and `fog!=I_Z`

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RD SHARMA-FUNCTION-Solved Examples And Exercises
  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) e...

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  3. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

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

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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 integ...

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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 given by f(x)=x^3+x is a bijection.

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  10. Let f: Nuu{0}vecNuu{0} be defined by f{n+1,if n is even n-1,if n is od...

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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: Rvec and g: RvecR be defined +1a n dg(x)=x-1. Show that fog=gof...

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  14. Verify assoiativity for the following three mappings : f: NvecZ0...

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

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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 (a) one-on...

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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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