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If \(f(x)=\dfrac1{x}\) and \(g(x)=\dfrac{x}{x^2+1}\) for all \(x>0,\) what is the minimum value of \(f(g(x))?\)

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If \(f(x)=\dfrac1{x}\) and \(g(x)=\dfrac{x}{x^2+1}\) for all \(x>0,\) what is the minimum value of \(f(g(x))?\)

by VJesus12 » Tue Sep 15, 2020 2:57 am

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If \(f(x)=\dfrac1{x}\) and \(g(x)=\dfrac{x}{x^2+1}\) for all \(x>0,\) what is the minimum value of \(f(g(x))?\)

(A) \(0\)

(B) \(\dfrac12\)

(C) \(1\)

(D) \(\dfrac32\)

(E) \(2\)

Answer: E

Source: Manhattan GMAT
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