Function Composite

This section has the following videos:

  • Lesson Video
  • Example Set A Practice Problems (Video Solutions)
  • Example Set B Practice Problems (Video Solutions)

The function operation that most algebra students dislike is the composite function.  However once algebra students learn to handle these problems they warm up to the topic.  A composite function is nothing more than evaluating a function with another function.  Lets take take the function f(x)=3x + 1.  If I said evaluate the function for x=3 you would write f(3) = 3(3) + 1.  Next you would figure out that 3(3) + 1 is equal to 10 and that would be the answer, f(3) = 10.  Now lets consider the same function but this time lets find f(y +4). Think carefully this would mean that in the function f(x)= 3x + 1 we would let x= (y + 4).  I know this is a little confusing so focus and stay with me.  Now going back to the function just replace the “x” with “(y + 4)” and simplify.  We get f (y + 4) =3(y + 4) + 1 and after we simplify we can write the result as 3y + 3(4) + 1 or 3y + 13.  The idea of evaluating a function with something other than a number is what trips up most students at first- yes it’s a little confusing.  But understanding how do work with functions and variables is key with composite functions.  Lets take that same function above f(x) = 3x + 1  and make up another function g(y) = y + 4.  If I say find f(g(y)) what I’m saying is plug in the g(y) function into the f(x) function and simplify- the process to solve this problem is the same as the example I did above f(y + 4) = 3(y + 4) + 1.  Ok take a deep breath and brush off any sweat, you can do this if you focus and practice- the notes below will help.