I have an inequality which has to be solved.

It has one variable whose range(domain) is known and I want to find out the resulting domain for the other variable with respect to this variable. Could someone suggest me how to do this? I have already checked solve function and did not find any method to define the original variable's domain.

Answer 1

[Roger Stafford]

The answer to this question depends very much on the nature of the relationship between the two variables. For the sake of this discussion, let's call x the first variable whose range is known and y the second variable whose range is to be determined. If y varies monotonically with x (always increasing or always decreasing as x increases,) then you need only find the two y values that correspond to the two ends of the x range (assuming the x range is a finite, closed interval.) If this is not the case you might look for values of y for which dy/dx is zero which could mark a boundary in the y range as a maximum or minimum, in addition to y values at the endpoints of the x range. If you are dealing with one or more inequalities involving x and y, the problem becomes more complicated but has similarities to the above reasoning. Suffice it to say that there is no general matlab method of answering your question to cover all possible relationships between variables.

[Aditya]

the variable x has range from [0,1]. And I don't know how y varies with respect to x. so is there no method covering this possibility?

[Aditya]

Sorry for this late info, but i found out that as x increases, y should also increase although no linearly.