Composite Functions

Find f(g(x))
g(x)=2x^2+4 and f(x)=x-2/4

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Jul 24, 2010
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by: Karin

As the title states, this is known as a composite function.

We are asked to find f(g(x)) where:

f(x) = x-2/4 and g(x) = 2x^2+4

So, step 1 is to substitute the value (2x^2+4) for g(x):

f(g(x)) = f(2x^2+4) - Substitute 2x^2+4 for g(x)

Now, we know that we need to find f(2x^2+4) for the function: f(x) = x-2/4

Step 2: Substitute (2x^2+4) for x.

f(2x^2+4) = (2x^2+4)-2
----------
4

Step 3: Simplify

2x^2+4-2 = 2x^2 +2
-------- -------
4 4

You can simplify further by dividing all terms by 2.

x^2 + 1 This is the final answer.
-------
2

I hope this helps,
Karin

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