Combination Of Functions

Arithmetic Combinations - A way to reorganize 2 functions (usually g or f) so they are easier to solve

1. (f±g)(x) = f(x)±g(x)

2. (fg)(x) = f(x)g(x)

3. (f/g)(x) = f(x)/g(x) ; g(x) ≠ 0

The compositions of f(x) with g(x) are solved the same way as any other funtion, except you plug "g" as x in the f(x) funtion

The composition of f(x) with g(x) is:

     f(g(x)) or (f◦g)(x)

ex #2)       f(x) = -3x     g(x) = 2x+6

          a.  find (f◦g)(x)

          b.  find (g◦f)(x)

          a.  f(g(x))                    b.  g(f(x))

               f(2x+6)                       g(-3x)

               -3(2x+6)                     2(-3x)+6

               -6x-18                        -6x+6

Links

An in-depth site that explains combinations of functions thoroughly.

Another in-depth site that explains combinations of functions.

Video