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 $b$.

As mentioned in the comments, we have $f(g(x)) = 2ax + 2b + 3 = x$. This is only true if $2a = 1$ and $2b + 3 = 0$, otherwise the equality wouldn't hold. Solving those, we get that $a = \dfrac{1}{2}$ and $b = -\dfrac{3}{2}$.
