max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|

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max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|

max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|
max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|

max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|
f(x)≥g(x)时,max{f(x),g(x)}=f(x)=1/2(f(x)+g(x)+f(x)-g(x))=1/2(f(x)+g(x)+|f(x)-g(x)|).
f(x)<g(x)时,max{f(x),g(x)}=g(x)=1/2(f(x)+g(x)+g(x)-f(x))=1/2(f(x)+g(x)+|f(x)-g(x)|).
所以,max{f(x),g(x)}=1/2(f(x)+g(x)+|f(x)-g(x)|).