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June 12th, 2007, 01:47 PM   #1
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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
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June 12th, 2007, 10:07 PM   #2
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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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