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

First, we show that $(f + g)oh = foh + goh$

L.H.S. $=$ $(f + g)oh = (f + g)[h(x)]$ $= f[h(x)] + g[h(x)] = foh + goh = R.H.S.$
Now, we show that $(f \cdot g)oh = (foh) \cdot (goh)$

L.H.S. $=$ $(f \cdot g)oh = (f \cdot g)[h(x)] = f[h(x)] \cdot g[h(x)] = (foh) \cdot (goh) = R.H.S.$