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FUNCTION OPERATIONS

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.

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FUNCTION OPERATIONS

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  1. FUNCTION OPERATIONS

  2. 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. For example: given f(x) = 3x – 2 and (f-g)(x) would be: 3x – 2 - Or simplified: 3x – 2 - - (fg)(x) would be: (3x – 2) Or simplified: 3 Or: 3- 4

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

  4. 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. For example: given f(x) = 3x – 2 and (f◦g)(x) would be: 3( )– 2 x +2 x +2

  5. 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. For example: given f(x) = 3x – 2 and x+2 x+2 Evaluate g(x+2) which becomes: We now evaluate f(x) as follows: 3( ) - 2

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