If f:R→R,g:R→R be two given functions then f(x)=2min{f(x)−g(x),0} equals
A
f(x)+g(x)−|g(x)−f(x)|
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B
f(x)+g(x)+|g(x)−f(x)|
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C
f(x)−g(x)+|g(x)−f(x)|
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D
f(x)−g(x)−|g(x)−f(x)|
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Solution
The correct option is Df(x)−g(x)−|g(x)−f(x)| We have, f(x)=2min{f(x)−g(x),0} ={0f(x)>g(x)2(f(x)−g(x))f(x)≤g(x) ={f(x)−g(x)−|f(x)−g(x)|f(x)>g(x)f(x)−g(x)−|f(x)−g(x)|f(x)≤g(x)∴f(x)=f(x)−g(x)−|f(x)−g(x)|