1. x/(abs. value of x)
2. x-(absolute value 5*x)
domain and range for these?
1. \({x\over{|x|}}=1\space or\space -1\)
When x is negative, it becomes -1
When x is positive, it becomes 1
So the domain is all x except 0 (not allowed to divide by 0) and the range is -1 and 1.
2. \(x-|5x|=-6x\space or\space -4x\)
For positive x, result is -4x
For negative x, result is -6x
In this case, domain is all x and the range is zero and below.
Because zero is allowed here and any x will yield a negative result.
