Question

If f, g, h are real valued functions defined on R, then prove that (f + g)oh = foh + goh. What can you say about fo(g + h) ? Justify your answer.

Answer 1

Let f + g = k 

Now k ⊙ h = k(h(x))

= (f + g((h(x)) 

= f[h(x)] + g [h(x)] 

= foh + goh 

(i.e.,)(f + g)(o)h = foh + goh

fo(g + h) is also a function