Question 1102474: the function “sgn b”, called the signum function, which is Latin for “sign”. For the purpose of this problem, we will define this function as follows:
sgnb={−1, b<0 } (the bracket should cover the whole thing)
{ 1, b≥0 }
For example, sgn(17) = 1, sgn(−√2) = −1, and sgn(0) = 1.
d) If b is any real number, how does the expression |b| sgn b simplify? Explain briefly.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!   
If  = any real number,
   , so  .
For non-negative numbers,  ,
the signum function returns 1,
the absolute value function returns the original number,
and the product of the returned values is the original number.
For negative numbers,
the signum function returns  ,
the absolute value function returns the positive opposite of the original number,
and the product of the returned values is the original number.
In other words, for negative numbers,
the absolute value takes away the minus sign,
but the signum function then reapplies the minus sign that the absolute value function took away.
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