Algebra - Functions

Question

given the equation xy + 3y = 2x + 1 show that y is a function of x and determine the domain in interval notation.

Answer 1

Factor out the y on the left side of the equation.

 

y(x + 3) = 2x + 1

 

 

Divide both sides of the equation by (x + 3).

 

y = (2x + 1) / (x + 3)

 

 

We have an equation that y is alone and all the x-terms are on the other side.

 

 

To find the domain of this function, set the denominator equal to zero.

 

x + 3 = 0

 

 

Solve for x.

 

x = -3

 

 

Domain is in the interval (-∞, -3)∪(-3, ∞).