What is the domain of f(x)=(y^2+1)/(y^2-2y) ?

The domain of f(x)=(y^2+1)/(y^2-2y) is y 2

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domain of f(x)=(y^2+1)/(y^2-2y)

domain

f (x) = \frac{y ^{2} + 1}{y ^{2} - 2 y}

y < 0 or 0 < y < 2 or y > 2

Interval Notation

(- \infty, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

y = 2, y = 0

The function domain

y < 0 or 0 < y < 2 or y > 2

What is the domain of f(x)=(y^2+1)/(y^2-2y) ?
The domain of f(x)=(y^2+1)/(y^2-2y) is y<0\lor 0<y<2\lor y>2