I am working through Khan Academy's calculus course and got stuck when the limits of composite functions came up. Say we want to find the limit of $f(g(x))$ as $x$ approaches one. The notation says that you plug $x$ into $g(x)$ and then plug $g(x)$ into $f$. Hence $f(g(x))$. But that doesn't find the limit at $1$. To be honest, I don't even know what the goal is with finding limits of composite functions. Are we trying to find the limit of $f$ or $g$? or both? If both, what does the limit of both mean in physical terms? Is it the rate of flow in a water pipe? The notation is unclear and makes the problem seem undefined to me. I would appreciate another explanation.
When finding the limit of a composite function, do you find the limit of the interior function and then the exterior function
calculuslimits
Best Answer
I figured it out. You are supposed to find the limit of the interior function and then use that limit as the x value for the exterior function while taking the limit of the exterior function. I was confused because the notation is wrong. Should have a lim in front of both g and f.