question_answer

If \[f:R\to R,g:R\to R\] be two given functions then \[h(x)=2\min \{f(x)-g(x),0\}\,\]equals

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 :

\[h(x)=2\min \{f(x)-g(x),0\}\] \[\therefore \]\[h\left( x \right)=f\left( x \right)-g\left( x \right)-|f\left( x \right)-g\left( x \right)|\]