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Question
6.5-2
If f(x)=x^2-4 and g(x)=-3x^2, find
f(x(x))

(yes, that's how it is written)

Thanks, much appreciated!

Answer
It seems to me that there is a typo in the problem.

f(x(x)) does not make sense, unless the "x(x)" means x*x=x^2, but then
why would they give g(x)?

If it is f(x^2), then it would be f(x^2)=(x^2)^2-4=x^4-4

If it is supposed to be f(g(x)), as I suspect, then it would be
f(g(x))=f(-3x^2)=(-3x^2)^2-4=9x^4-4

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Abe Mantell

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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

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Over 15 years teaching at the college level.

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NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

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B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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