mathcalculus
posted by Shreya on .
the absolute value function
g(x) = 5x can be written as a piecewise function. the piecewise function which represents g(x) is
this have to be g(x) = x5 if x be greater to or equal to five. and the negative piece have to be 5x. does it matter if i write 5+x instead of 5x?
which of following is root of equation 3x1 = 5
i get 4/3 for this.

from x = oo to x = 5
g = 5 + x
from x = 5 to x = oo
g = x  5
3x1 = 5
3 x = 4
x = 4/3 
thank you for the 3x1 = 5 it says in back of book that there are no roots of the equation 3x1 = 5 and i not see how that be possible.

By definition
 anything  has to be a positive number or at least zero
so 3x1\ = 5 would contradict the very definition of absolute value,
So without even showing a single step, we can say that there is no solution.
if you verify your answer of 4/3, ...
LS = 3(4/3)  1
=  5
= +5
RS = 5
LS ≠ RS , so .... no solution