* Question for discrete math:functions,recurrence relation

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The discussion focuses on determining the properties of the function f:N*N->Q defined by f(m,n)=(m-3)/n, specifically whether it is injective or surjective. It also addresses the composition of bijective functions, stating that if f:A->B and g:B->C are both bijective, then their composition (g o f):A->C is also bijective. Additionally, there is a recurrence relation a(r)-5a(r-1)+6a(r-2)=2^r+r that needs solving. Participants are reminded that this is a "no homework" forum, suggesting that such problems should be posted in a designated homework forum instead. The conversation emphasizes the importance of understanding function properties and recurrence relations in discrete mathematics.
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a) Let f:N*N->Q be defined by f(m,n)=(m-3)/n. Determine if f is injective or surjective.

b) Show that if f:A->B and g:B->C are both bijective, then the composition (g o f):A->c is also bijective.

Solve the recurrence relations

a(r)-5a(r-1)+6a(r-2)=2^r+r
(r,r-1,r-2 are all subscripts)
 
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Since this is a "no homework" forum, you should ask again in the "homework" forum.
 
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