FUNCTION OPERATIONS

Students seem to understand that the following: (f+g)(x) means add the f(x) and the g(x) functions together. (fg)(x) mean multiply the f(x) and the g(x) functions together. (f/g)(x) means divide them and (f-g)(x) means subtract them.

What students sometimes struggle with is: (f◦g)(x) which means substitute the g(x) into the f(x) functions and simplify. (f◦g)(x) would be: 3( )– 2 This process is call a composition of functions.

Another instance where students sometimes struggle is as follows: (f◦g)(x+2) which means after you have completed the composition of f and g THEN substitute x+2 for ALL the “x”’s in the PINK function and simplify. (f◦g)(x) would be: 3( )– 2 x +2

You could also complete this composition by the following method: (f◦g)(x+2) which means substitute x+2 into the g(x) and THEN substitute this NEW g(x) into the f(x) functions and simplify. Evaluate g(x+2) which becomes: x+2 We now evaluate f(x) as follows: 3( ) - 2