2.4.2 So­lu­tion math­ops-b


If, say, $\widehat{x^2}\sin(x)$ is sim­ply the func­tion $x^2\sin(x)$, then what is the dif­fer­ence be­tween $\widehat{x^2}$ and $x^2$?


Noth­ing that af­fects the price of eggs. Just the way you think about them. You think of $\widehat{x^2}$ as the op­er­a­tor that turns a func­tion like $\sin(x)$ into the func­tion $x^2\sin(x)$. But you think of $x^2$ as a recipe that turns a value like 3 into $3^2$ $\vphantom0\raisebox{1.5pt}{$=$}$ 9.