Find the domain of the variable x for which the following equation determine y as a real function of x.
y - xy = 5
y(1-x)=5
y=5/(1-x) where x is not equal to 1
domain of x: all real values of x not equal to 1.
To determine the domain of the variable x for which the equation determines y as a real function of x, we need to find the values of x that satisfy the equation.
Let's solve the equation step-by-step:
1. Start with the equation: y - xy = 5
2. Rearrange the equation to isolate y: y = xy + 5
3. Now, we have y as a function of x: y = f(x) = xy + 5
To determine the domain, we need to find the values of x for which this function is defined and gives real values of y. In other words, we need to find the values of x that do not result in any mathematical inconsistencies, such as division by zero or taking the square root of a negative number.
In this case, there are no such restrictions or limitations on x. Therefore, the domain of x is all real numbers, or (-∞, ∞).