1boss this is simple:
\left|f(x)+g(x) \right|=
\left|f(x) \right|+\left|g(x) \right|
only if f(x) and g(x) have the same sign
which implies that f(x).g(x)>=0 ....the equality holding for either of the functions being zero
I just came across a statement :
If |f(x)+g(x)| = |f(x)| + |g(x)|
then f(x).g(x) ≥ 0
What does this mean ?
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5 Answers
1if g(x) is not equal to / less than -f(x)
then equality holds!!!!
check it if i m crrt.
i think they want to tell that none of the func. r odd.
11see basically mod tells us the magnitude
consider two functions which have opposite signs
now if we consider the two functions within mod that is without splitting then as there is a '+' sign in between hence the sign of no function gets altered and as the two functions have opposite signs then one function will tend to decrease the overall value but by splitting it this decreasing effect gets neglected...hence both must have same sign and hence their product must not be negative
