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Question

If f:RR and g:RR be two given functions, then 2 min 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 D

f(x)-g(x)-g(x)-f(x)


Explanation for the correct answer:

Step 1: Case 1, when f(x)>g(x)

Let h(x)=2minf(x)-g(x),0

f(x)>g(x)f(x)-g(x)>02minf(x)-g(x),0=0

Therefore, h(x)=0

Step 2: Case 2, when f(x)<g(x)

f(x)<g(x)f(x)-g(x)<02minf(x)-g(x),0=2min(f(x)-g(x))

h(x)=2(f(x)-g(x))

Therefore, h(x)=f(x)-g(x)-g(x)-f(x)

Hence, the correct answer is option (D).


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