Many students can not see it in real life why FoG(x) exist but GoF(x) does not exist.
They do not have clear idea of domain & range of the functions.
Domain – The set of numbers where the given function works/exists.
Math example F(x) = sinx , here we expect our domain to be angles.
Real life example – F(x) = Toaster, Bread, pitta, tomato, potato belongs to the domain. I am sure, people wont prefer to put water in Toaster so , water does not belong to the domain of toaster.
Range is what we get as an output of that function.
Math example F(x) = sinx , Range will be [-1,1]
Real life example – F(x) = Toaster. Toasted Bread, toasted pitta, roast tomato, roast potato belongs to the range.
If the domain and range is clear now, then we are in a state to move forward and explore why sometimes “FoG(x) exist but GoF(x) does not exist.”
FoG arrangement is like , 2 machines kept next to each other. First, machine G and then Machine F. x goes into Machine G and G(x) comes out, now this G(x) goes in machine F.
If this G(x) is not a suitable input for F or in mathematical language – if the range of G(x) is not domain of F(x) then FoG(x) does not exist.
