Track / Stage 5 / 193 of 400 #793 of 2000

Question: Let $x, y, z \in(0,+\infty)$, and $x^{2}+y^{2}+z^{2}=$ 1, find the range of the function $f=x+y+z-x y z$.

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Official solution

On the one hand, from the known conditions we have $x, y, z \in (0,1)$,
$$y > y^{2}, z > z^{2}, y^{2} + z^{2} = 1 - x^{2} .$$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.