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f : Z rarr Z and g : Z rarr Z. Defined a...

`f : Z rarr Z and g : Z rarr Z`. Defined as `f(n) = 3n` and `g(n) = {{:(n/3",","If n is a multiple of 3"),(0",","If n is not a multiple of 3"):} AAninZ` Then show that `gof = I_z` but `fog ne I_z`

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. If f is greatest integer function and g is a modulus functions the fin...

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  2. f:R rarrR , f(x) =x/(sqrt(1+x^2)),AAx inR. Then find (fofof) (x).

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  3. f : Z rarr Z and g : Z rarr Z. Defined as f(n) = 3n and g(n) = {{:(n/3...

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  4. f: R rarrR be defined by f(x) =x/2+3, g: R rarr R be defined by g(x) ...

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  5. f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n...

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  6. ** is a binary operation on the set Q. a"*"b = (2a+b)/4 then find 2"...

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  7. ** is a binary operation on the set Q. a"*"b=a+12b+ab then find 2"*...

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  8. ** is a binary operation on the set Q. a"*"b=(a)/2+b/(3) then find ...

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  9. ** is a binary operation o Z. If x"*" y = x^(2)+y^(2)+xy then find [(...

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  10. ** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b...

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  11. Show that addition and multiplication are associative binary operation...

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  12. Find the identity element , if it exists for the following operation ....

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  13. Find the identity element , if it exists for the following operation ....

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  14. Find the identity element , if it exists for the following operation ....

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  15. Find the identity element , if it exists for the following operation ....

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  16. Find the identity element , if it exists for the following operation ....

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  17. Find the identity element , if it exists for the following operation ....

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  18. Find the identity element , if it exists for the following operation ....

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  19. On R - {-1}, a binary operation ** defined by a"*"b = a + b +ab then f...

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  20. ** be a binary operation on a set {0,1,2,3,4} defined by a**b={(a+b,...

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