Hello,

Solution:

f(x)=px+q, g(x)=rx+s

f(g(x))= p g(x) +q = p(rx+s) + q = prx+ps+q

g(f(x))= r f(x) + s = r(px+q) + s = prx+qr+s

f(g(x)) = g(f(x))

prx+ps+q = prx+qr+s

ps+q = qr+s

Now, given that-

f(x) = px+q

f(s) = ps+q  [Since x=s]

And,

g(x) = rx+s

g(q) = rq+s  [Since x=q]

Therefore, f(g(x)) = g(f(x)) is f(s) = g(q)

Hope this helps!!!