Posted by Joel on October 24, 2002 at 22:39:07:
In Reply to: Composition of Functions posted by John on October 24, 2002 at 21:49:15:
: How do I evaluate the functions f(x) = -2x and g(x)= x squared -3, graphically. How do you know what happens to the graphs during (f+g)(x) and (f-g)(x)
Your example is not composition; it is combination of functions. Composition would be (f of g)(x), usually written with little tiny "o" instead of "of".
(f+g)(x) is defined as f(x) + g(x) and (f-g)(x) is f(x)-g(x). You have to be careful of the domains, though. If the domain of f is A and the domain of g is B, the domains of f+g and f-g are {A intersection B}. As far as your example is concerned, domain is not an issue since both of your functions are continuous over the set of real numbers, so the domains of f+g and f-g are also.
So just add 'em & graph 'em:
(f+g)(x) = y = x^2 - 2x -3
and
(f-g)(x) = y = 3 - 2x - x^2