posted by ayotal on .
when working with composite functions, does fog=gof? how do i create two functions,f(x) and g(x) to show that this statement is either true or false.i need to explain my reasoning
In mathematics, you cannot prove that a statement is true by a finite number of examples, because it is not possible to prove all possible cases by a finite number of examples.
However, to prove that a statement is false, you only need ONE counter-example. This is probably your case here.
Since we demonstrated fog(x)≠gof(x), the given statement is not true.
On the other hand, if we define
so fog(x)=gof(x) in this case, BUT it does not prove anything.