Range of a Three Variable Fun-ction !!

Algebra Level 5

\(If\quad the\quad range\quad of\quad a\quad three\quad variable\quad function\\ \quad \quad \quad \quad \quad \quad \quad \boxed { f\left( x,y,z \right) \quad =\quad \frac { xy+yz+xz }{ { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } } } \quad \\ can\quad be\quad written\quad as\quad \left[ a,b \right] .\quad Find\quad a+b.\\ \)

Note: \( (a, b, c) \neq (0, 0, 0) \). The values could be negative.

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