Mapping/K/Translation in domain and codomain/Equivalence relation/Exercise

Let ${}K$ be a field, and let

${}\operatorname {Map} \,{\left(K,K\right)}={\left\{f:K\rightarrow K\mid f{\text{ function}}\right\}}\,$

be the set of all mappings from ${}K$ to ${}K$. We consider the relation on ${}\operatorname {Map} \,{\left(K,K\right)}$ defined by ${}f\sim g$ if there exist ${}c,d\in K$ such that

${}f(x)=g(x+c)+d\,$

holds for all ${}x\in K$. Show that this is an equivalence relation.

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