Mapping set/R/Operations/Distributivity laws/Exercise

We consider the set

${}M=\operatorname {Map} \,{\left(\mathbb {R} ,\mathbb {R} \right)}\,,$

which is, with the pointwise addition ${}+$ of functions, a commutative group. On this set, the composition of mappings ${}\circ$ gives an associative operation, with the identity as neutral element.

1. Show that the distributive law in the form

   ${}(f+g)\circ h=f\circ h+g\circ h\,$

   holds.

2. Show that the distributive law in the form

   ${}h\circ (f+g)=h\circ f+h\circ g\,$

   does not hold.

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