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f: Z rarrZ and g : Z rarrZ are defined a...

`f: Z rarrZ and g : Z rarrZ` are defined as follow :
`f(n) ={:{(n+2," n even"),(2n-1," n odd"):}, g(n) ={{:(2n,"n even"),((n-1)/2,"n odd"):}` Find fog and gof.

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The correct Answer is:
(fog)(n) = `{{:((2n+2),"n even"),((n+3)/2,"n odd , n = 4K+1"),(n-2",","n odd , n = 4K +3"):}`
(gof) (n) = `{{:(2n+4",","n even"),(n-1","," n odd"):}`
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. f : Z rarr Z and g : Z rarr Z. Defined as f(n) = 3n and g(n) = {{:(n/3...

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

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

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

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

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

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

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

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

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

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  11. Find the identity element , if it exists for the following 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. On R - {-1}, a binary operation ** defined by a"*"b = a + b +ab then f...

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

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  19. On Z ** defined by a**b = a+b+1 . Is ** associative ? Find identity el...

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  20. ** be binary operation defined on a set R by a**b=a+b-(ab)^2. Show tha...

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