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June 12th, 2007, 01:47 PM  #1 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  Composite of f, g, and/or h.
Let f(x) = x^2, g(x) = 3x and h(x) = (sqrt{x}) + 1. Express the function as a composite of f, g and/or h. p(x) = 3(sqrt{x}) + 3 
June 12th, 2007, 10:07 PM  #2 
Newbie Joined: Jun 2007 Posts: 6 Thanks: 0 
f(x) > square something g(x) > multiply something by 3 h(x) > take the square root of something and add 1 p(x) = 3*sqrt(x) + 3 1. Is something being squared? Possibly x^(1/4). Not likely. Move on. 2. Is something being multiplied by 3? Let's try by dividing by 3. p(x) / 3 = sqrt(x) + 1 Hmmmm. Now to get it back.... multiply by three, which is the same thing as applying g(x) p(x) = [p(x) / 3] * 3 = [sqrt(x) + 1] * 3 = g(sqrt(x) + 1) 3. Now we have g(sqrt(x) + 1) Let's look at h(x). Is anything having its square root taken and 1 added? It looks like that's true for x. g(sqrt(x) + 1) = g( h(x) ) And g( h(x) ) is your answer. 

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