Calculus/function

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Expert: - 1/17/2011


Question
Let f(x) = x/x-5.  Find a function y = g(x) so that (f o g)(x) = 3x.

g(x) = ?

Answer
f(g(x)) = 3x

f(g(x)) = g(x)/(g(x)-5)

So g(x)/(g(x)-5) = 3x

g(x) = (3x)(g(x)-5)

g(x) = 3xg(x) - 15x

15x = 3xg(x) - g(x)

15x = g(x)(3x-1)

g(x) = 15x/(3x-1)

You can check this answer by substituting
15x/(3x-1) for x in x/(x-5) , you will get 3x

Calculus

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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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Ph.D. in Mathematics and many years teaching Calculus at state universities.

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