Answer:
Let
be any
element
=
f(h(x)+ g(h(x))
=
(foh) (x) + (goh) (x)
=
(foh + goh) (x)
=
(foh + goh) (x)
Also,
((f.g) oh) (x) = (f.g) (h(x))
=
f(h(x)).g(h(x))
=
(foh)(x). (goh)(x)
=
((foh).(goh) (x)
which
is proved.
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