Question

Let f,g and h be functions from R to R. Show that (f+g)oh =foh+goh

Answer 1

To prove (f+g)oh =foh +goh
Consider
LHS =((f+g)oh)(x)=(f+g)(h(x))
=f(h(x))+g(h(x))=(foh)(x)+(goh)(x)=((foh)+(goh))(x)
$\therefore \left(\right(f+g\left)oh\right)\left(x\right)=\left(\right(foh)+(goh\left)\right)\left(x\right)\forall x\in R$
Hence, (f.g)oh=(foh)+(goh)