Question

if f(x) = px+q, g(x) = rx+s and f(g(x)) = g(f(x)), then​

Answer 1

plz complete the question ....

Answer 2

Step-by-step explanation:

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!!!