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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

Answer
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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I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.

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I am a PhD educated mathematician working in research at a major university.

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Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

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BA mathematics & physics, PhD mathematics from a top 20 US school.

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Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

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In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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