The function \(f\) is defined as \(f(x,y) = xy\) for positive numbers \(x\) and \(y.\) If

The function \(f\) is defined as \(f(x,y) = xy\) for positive numbers \(x\) and \(y.\) If \(f\left(x,\dfrac1{x}\right)=f(x,y),\) which of the following must be true?

A. \(f(x,x)=f(y,y)\)

B. \(f\left(x,\dfrac1{x}\right)=f\left(x,\dfrac1{y}\right)\)

C. \(f\left(x+y,\dfrac1{x}\right)=f\left(x+y,\dfrac1{y}\right)\)

D. \(f(x^2,y^2)=f\left(y(x+1),\dfrac1{y+1}\right)\)

E. \(f\left(x,\dfrac1{y}\right)=1\)

Answer: D

Source: e-GMAT