Let $f(x) = 2x - 3$ and $g(f(x)) = 5-4x.$ Find $g(4).$
To find $g(4)$, I need to first figure out what value of $x$ makes $f(x) = 4$. I can do this by solving the equation $2x - 3 = 4$ for $x$. Adding $3$ to both sides, I get $2x = 7$. Dividing both sides by $2$, I get $x = 3.5$. So $f(3.5) = 4$. Now I can plug in $x = 3.5$ into $g(f(x)) = 5 - 4x$. I get $g(f(3.5)) = g(4) = 5 - 4(3.5)$. Simplifying, I get $g(4) = 5 - 14 = -9$. 