Let $f(x) = 2x + 3$ and $g(x) = ax + b$. If $f(g(x)) = x$ for all $x$, determine $a$ and $b$ This is what I know:
$f(x) = 2x + 3$
$g(x) = ax+b$
$f(g(x)) = 2(ax+b) + 3 = x$
I am just not too sure what to do next to find $a$ and $b$.

Since $$f(g(x))=x$$ for all $x$, it is true also for $x=0$:  $$2b+3=f(b)=f(g(0))=0$$
and the same is true for $x=1$:
$$ 1= f(g(1))= f(a+b) = 2(a+b)+3$$
