Maths problem

y=(1-2x)^(-1/3)=1/(1-2x)^(1/3)

x cannot be 1/2 (undefined--division by zero)
if x>1/2 then y is negative
if x<1/2 then y is positive
so the range of x is all real numbers except 1/2

Rap

rap

there's sth you missed out...
the answer is obviously NOT what you've calculated.. i would have no problem on the solution if the answer is that obvious...

the answer is lxl < .5

Cube root of a negative number
You can take the cube root of a negative number, so I don't see the issue with Rap's answer. If x is 9/16 then 1-2x = -1/8. (-1/8)^(-1/3) = -8 ^(1/3) = -2. You will never get your calculator to pull that off, but it works on paper.

You wanna 'splain that Lucy.

the cube root of a negative number is a negative number.

Getting my definition problem out of the way, the range of x are all defined x's in the domain of y.
that is
x=1/2-1/2y^3
and the domain of y are real numbers where y<>0
The range of x is expressed as y goes to -0, x goes to +infinity as y goes to -0, x goes to -infinity

Rap