Question

Given the equation xy+4y=3x-2 show that y is a function of x and determine the domain in interval notation.

Answer 1

First, the equation has to be rearranged so that y will be isolated on the left-hand side of the equation.


(x + 4)y = 3x - 2y = (3x - 2)/(x + 4)

This form is a rational function which is of course a function. All values of x are possible, except for x when y becomes undefined, thus the domain should be x /= -4. In interval notation, (-inf, -4) U (-4, inf).


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