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If f: RvecRvecR are two given functions,...

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

A

f(x) + g(x) - |g(x) - f(x)|

B

f(x) + g(x) + |g(x) - f(x)|

C

f(x) - g(x) + |g(x) - f(x)|

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
`f : R rarr R, g : R rarr R`
f(x) = 2 min f(x) - g(x), 0
Let f(x) - g(x) `gt` 0, then
F(x) = f(x) - g(x) - |f(x) - g(x)| and f(x) - g(x) `lt` 0, then
F(x) = 2[F(x) - g(x)] = [f(x) - g(x)] - |f(x) - g(x)|
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