If f(x)=x-5 and g(x)=3x+11, find (f+g)(x).
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Answer:
The answer is .
Step-by-step explanation:
First, it is important to recall that the group law is not commutative in general, so we cannot assume it here. In order to solve the exercise we need to remember the axioms of group, specially the existence of the inverse element, i.e., for each element there exist another element, denoted by
such that
, where
stands for the identity element of G.
So, given the equality we make a left multiplication by
and we obtain:
But, . Hence,
.
Now, in the equality we make a right multiplication by
, and we obtain
.
Recall that and
. Therefore,
.