Maximum and minimum of the inequality

[Гост]

If [tex]\displaystyle f(x,y,z) = \frac{x+1}{xy+x+1}+\frac{y+1}{yz+y+1}+\frac{z+1}{xz+z+1}[/tex].

Then Maximum and Minimum of [tex]f(x,y,z)[/tex]

Where [tex]x,y,z\geq 0[/tex]

[Xixibg]

[tex]f_{max}(x,y,z)=3 ,(x=y=z=0)[/tex]
[tex]f_{min}(x,y,z)=0 ,(lim_{x,y,z->\infty }f(x,y,z)=0)[/tex]