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# Advanced Math/Breakdown of Composite functions (precalculus)

Question
Hi Clyde, if f o g o h(x) is cos^2(x+7), What is f(x), g(x), and h(x)? I understand that h(x)=x+7 but I don't know if cos(cos(x))=cos^2(x) or in other words how to get from g(x)to f(x)
Many Thanks, Sam

Every function can be thought of as an action, something you do to the input.

For example, the function you give h(x)=x+7 is the function that adds 7 to x.

So you have to think "what is the next thing I do to x?"

The next thing is the cosine. So g(x)=cos(x).

The next thing you do is square it, so f(x)=x^.

That way, when you do f o g o h (x), first you add seven, then cosine, then square.

x
x+7
cos(x+7)
cos(x+7)^2

Note: cos^2(x) means [ cos(x) ]^2

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#### Clyde Oliver

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