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

[VJesus12]

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