
Mapping (functions)
Find the values of x such that the function $\displaystyle f^{2}$ maps onto $\displaystyle g$.
So we need to solve the equation $\displaystyle f^{2}(x)=g(x)$.
My students asked me why is that the equation to be solved. They don't understand about the "maps onto" part.
How should I explain this? a simple and straightforward explanation?
Thanks for sharing :)

I may be off I haven't taken math classes in years, but it seems to me that "maps onto" in this case is another way to say intersects with. As in at what x value do the 2 functions have the same y value. So you set them equal to each other and solve for x.
"Maps onto" is more useful if talking about 3 dimensions where a 3d object intersects a plane, and leaves what we see as a 2d map when we look at all the points of intersection. Think of a sphere intersection a plane. We would see a map of a circle.