A) \[f(x)+g(x)-\left| g(x)-f(x) \right|\]
B) \[f(x)+g(x)+\left| g(x)-f(x) \right|\]
C) \[f(x)-g(x)+\left| g(x)-f(x) \right|\]
D) \[f(x)-g(x)-\left| g(x)-f(x) \right|\]
Correct Answer: D
Solution :
[d] \[f:R\to R,\,\,\,g;R\to R\] We know that min. \[\{{{f}_{1}}(x),{{f}_{2}}(x)\}\] \[=\frac{({{f}_{1}}(x)+{{f}_{2}}(x))-\left| {{f}_{1}}(x)-{{f}_{2}}(x) \right|}{2}\] \[\therefore \min \{f(x)-g(x),0\}\] \[=\frac{(f(x)-g(x)+0)-\left| f(x)-g(x)-0 \right|}{2}\] \[=\frac{(f(x)-g(x))-\left| f(x)-g(x) \right|}{2}\]
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