Hello, thereddevils!
IThink is absolutely correct . . .
Solve this inequality: .$\displaystyle x2 \:<\:\tfrac{1}{x}$ The graph of $\displaystyle f(x) \:=\:x2$ is a Vshaped graph with its vertex at (2,0).
The graph of $\displaystyle g(x) \:=\:\tfrac{1}{x}$ is a hyperbola in the 1st and 3rd quadrants. Code:

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The graphs intersect at: $\displaystyle P\left(1\!+\!\sqrt{2},\:\sqrt{2}\!\!1\right)$
We see that $\displaystyle f(x) < g(x)$ on the interval: .$\displaystyle \left(0,\:1\!+\!\sqrt{2}\right)$