Math Archive (13)

Calculus Level 5

$\large F(x) = \left(1 + \dfrac1x\right)^x , \quad G(x) = \left(1 + \dfrac1x\right)^{x+1}$

Given the two functions above for all $x> 0$ . Which of the following is an increasing function for positive $x$ ?

This question is submission of Problem Writing Party (May 2016).

F(F(x)-G(x))

G(F(x))

G(F(x)-G(x))

G(x)-F(x)

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