Let $f(x) = ax + b$ and $g(x) = cx + d$, where $a, b, c, d$ are constants. Determine for which constants $a, b, c, d$ it is true that $f ◦ g = g ◦$

Question

I'm working on this question and this what I did I get $f•g(x) = f(cx+d)=a(cx+d) + b = acx +ad + b $ $g•f(x) = g(ax+b) = c(ax+b) + d = acx + cb + d $ So how to I get $f•g = g•f$?

Well, set the two things you got equal to each other first of all... — anon, Apr 21 '16 at 02:22
You cannot ask "then what's next"? within a minute of getting a suggestion. You need to think things through. — pjs36, Apr 21 '16 at 02:27

score 1 · Answer 1 · answered Apr 21 '16 at 02:24

1

We would like that $$ acx+ad+b=acx+bc+d, $$ for all $x$, thus

$$ ad-bc=d-b. $$

answered Apr 21 '16 at 02:24

Olivier Oloa

120,989

I suppose it must be ad-d=bc-b factoring we get d(a-1)=b(c-1). – Surdz Apr 21 '16 at 02:44

Let $f(x) = ax + b$ and $g(x) = cx + d$, where $a, b, c, d$ are constants. Determine for which constants $a, b, c, d$ it is true that $f ◦ g = g ◦$

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