What is the domain of f(x,y)=sin((x-3)/(x-5)) ?

The domain of f(x,y)=sin((x-3)/(x-5)) is x 5

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domain of f(x,y)=sin((x-3)/(x-5))

domain

f (x, y) = sin (\frac{x - 3}{x - 5})

x < 5 or x > 5

Interval Notation

(- \infty, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5

The function domain

x < 5 or x > 5

f (x) = \frac{5}{x ^{2} + 1}

y = x^{2} y = - 2 x + 8

f (x) = 27 x^{3} - 9 x + 9

f (x) = (9 - x^{2})^{\frac{3}{2}}

f (x) = x^{3} - 27 x + 10

What is the domain of f(x,y)=sin((x-3)/(x-5)) ?
The domain of f(x,y)=sin((x-3)/(x-5)) is x<5\lor x>5