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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
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
