Question

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Answer 1

x⊕e=x
xe+2x+2e+2=x
xe+2x-x+2e+2=0
xe+x+2e+2=0
x(e+1)+2(e+1)=0
(e+1)(x+2)=0
e+1=0
e=-1,∀x∈R

Answer 2

[tex]\it x \circ e=x \Rightarrow xe+2x+2e+2=x \Rightarrow e(x+2) +(x+2) =0 \Rightarrow \\\;\\ \Rightarrow (x+2)(e+1) =0 \Rightarrow e+1=0 \Rightarrow e=-1[/tex]