Homework Help Forum: Math Analysis

Posted by Emily on Wednesday, October 14, 2009 at 11:00pm.

Let f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x. Express the following function k as a composite of three of these four functions. k(x)= sqrt (x^3 - 4) Do I need to factor anything out of the parentheses or something? If you can, please explain this problem to me :) any help is GREATLY appreciated!!

• Math Analysis - MathMate, Wednesday, October 14, 2009 at 11:09pm

  The composition of functions can be expressed as the function of a function. Let f(x)=x² and g(x) = x+1, fog(x) = f(g(x)) = f(x+1)=(x+1)² gof(x) = g(f(x)) = g(x²) = x²+1 So it is clear that in general fog(x) ≠ gof(x). You can read more about it in this article: http://en.wikipedia.org/wiki/Function_composition Given f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x. You can "compose" the function m(x) = x³-4 from m(x) = hof(x) = h(f(x)) = h(x³) = x³-4 Can you take it from here?

  
  

• Math Analysis - Emily, Thursday, October 15, 2009 at 1:30am

  Ohhh that makes perfect sense! I don't see how I couldn't see that before. Soooo the answer would be g(h(f(x))), right? Thanks for your help!! :D :D

  
  

• Math Analysis - MathMate, Thursday, October 15, 2009 at 6:50am

  Glad to be of help!

  
  

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