how do you find the inverse of (f of g)(x)??

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how do you find the inverse of (f of g)(x)??

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## Answers (1)

first, you have to find (f of g)(x), so you plug g(x) into x for f(x)

f(g(x))= (5000/(x^2+1))+7

you can't really simplify that, so then you take the inverse by switching y and x

x=(5000/(y^2+1))+7

then, you want to isolate the y

x-7=5000/(y^2+1)

(x-7)(y^2+1)=5000

y^2+1=5000/(x-7)

y^2=(5000/(x-7))-1

y=√ [(5000/(x-7))-1]

Reference:math class