If And for all Then
Proof
Apply Proving fâ(0) has f as constant function theorem to Then Thus is a constant function
As h is a constant, we can denote is as so
If a<b And fâ˛(x)=gâ˛(x) for all xâ(a,b) Then f(x)=g(x)+c
Apply Proving fâ(0) has f as constant function theorem to h=fâg Then hâ˛(x)=fâ˛(x)âgâ˛(x)=0 Thus h(x) is a constant function
f=h+g As h is a constant, we can denote is as h=c so f(x)=g(x)+c