Explanation:
these are composite functions : a function of a function of a value.
this can have many more "staging" levels.
in essence, we calculate the functional result of the innermost function (with the given value) first, use that functional result as input value for the next function to the left. use that functional result as input value for the next function to the left. ...
f(g(x)) means therefore we start with g(x).
g(f(x)) means we start with f(x).
that is all. it is really simple. and actuality fun (like a maze - remember e.g. computer games, where you walked through one door and excited through a totally different door ?).
f(g(0)) =
so, we need g(0) = 4 - 0² = 4
and now we calculate
f(4) = 7×4 + 6 = 28 + 6 = 34
therefore,
f(g(0) = 34
g(f(0)) =
so, we need f(0) = 7×0 + 6 = 6
and now we calculate
g(6) = 4 - 6² = 4 - 36 = -32
therefore,
g(f(0)) = -32