Show that max$\{$f$,$ g$\}=\backslash$Theta $($f $+$ g$)$

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To show that max$\{$f$,$g$\}=\backslash$Theta $($f$+$g$)\backslash$max$\backslash \{$f$,$ g$\backslash \}=\backslash$Theta$($f $+$ g$)$max$\{$f$,$g$\}=\backslash$Theta $($f$+$g$),$ we need to find constants c$1,$c$2,$c$\_1,$ c$\_2,$c$1,$c$2,$ and n$0$n$\_0$n$0$ such that:

c$1($f$($n$)+$g$($n$))<=$max$\{$f$($n$),$g$($n$)\}<=$c$2($f$($n$)+$g$($n$))$c$\_1($f$($n$)+$ g$($n$))\backslash$leq $\backslash$max$\backslash \{$f$($n$),$ g$($n$)\backslash \}\backslash$leq c$\_2($f$($n$)+$ g$($n$))$c$1($f$($n$)+$g$($n$))<=$max$\{$f$($n$),$g$($n$)\}<=$c$2($f$($n$)+$g$($n$))$ for all n$>=$n$0$n $\backslash$geq n$\_0$n$>=$n$0.$