SOLUTION: Hello, Problem: Given the equation xy + 3y = 2x + 1, show that y is a function of x and determine the domain in interval notation. Thank you in advance, Ryan

Algebra ->  Functions -> SOLUTION: Hello, Problem: Given the equation xy + 3y = 2x + 1, show that y is a function of x and determine the domain in interval notation. Thank you in advance, Ryan       Log On


   

Question 905083: Hello,
Problem:
Given the equation xy + 3y = 2x + 1, show that y is a function of x and determine the domain in interval notation.
Thank you in advance,
Ryan

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First solve for y

xy+%2B+3y+=+2x+%2B+1

y%28x+%2B+3%29+=+2x+%2B+1

y+=+%282x+%2B+1%29%2F%28x+%2B+3%29

The function is y+=+%282x+%2B+1%29%2F%28x+%2B+3%29 which can also be written as f%28x%29+=+%282x+%2B+1%29%2F%28x+%2B+3%29 (since y = f(x))

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You cannot divide by zero. So x%2B3, the denominator, can't be equal to zero. Set it equal to zero and solve for x

x%2B3=0

x=-3

The value x=-3 causes the denominator to be zero. Therefore, we must kick it out of the domain. Any other real number is perfectly fine since it doesn't cause a division by zero error.

Domain: Set of all real numbers x such that x%3C%3E-3

Domain in interval notation: