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If `f: RvecRvecR` are two given functions, then prove that `2m indot{if(x)-g(x),0}=f(x)-|g(x)-f(x)|`

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If `f: RvecRvecR` are two given functions, then prove that `2m indot{if(x)-g(x),0}=f(x)-|g(x)-f(x)|`
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`h(x)= 2 min. {f(x)-g(x),0}`
`={(0",",f(x) gt g(x)),(2{f(x)-g(x)}",",f(x) leg(x)):}`
`={(f(x)-g(x)-|f(x)-g(x)|",",f(x) gt g(x)),(f(x)-g(x)-|f(x)-g(x)",",f(x) leg(x)):}`
` :. h(x)=f(x)-g(x)-|g(x)-f(x)|`
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