Needed help with this math question.

Question

f(y)= y+1/y^2 - y

What is the domain of this function?

Answer 1

The restriction on the domain of a rational function (function in which the variable occurs in the denominator), is all values of the variable that make the denominator 0.

As the equation is written, the denominator is y².  If we set the denominator equal to 0 we have:

y² = 0

By taking the square root, we get the answer:

y = 0

The domain of the equation (as you wrote it) is y ≠ 0.

 

In case you meant to write the function as:

f(y) = (y + 1)/(y² - y)

The denominator would then be y² - y

y² - y = 0

Factoring produces:

y(y - 1) = 0

Solving each of the factors for y gives us:

y = 0 and y = 1

The domain of this function is y ≠ 0 and y ≠ 1.