How to establish the ff. properties of δ(y) ?

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deah

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please help me how to
Establish the ff. properties of δ.
(a) δ = δ(-y)
(b) δ = δ'
(c) yδ= 0
(d) δ(ay)= 1/a δ
(e) δ(y²-a²) = [1/(2a)] [δ(y-a)+δ(y+a)]
(g) δ δ(y-a) = f(a) δ(y-a)
(h) yδ' = -δ
 

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