What is the domain of f(x)=sqrt((x^2-5x+6)/(x-3)) ?

The domain of f(x)=sqrt((x^2-5x+6)/(x-3)) is 2 3

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domain of f(x)=sqrt((x^2-5x+6)/(x-3))

domain

f (x) = \frac{x ^{2} - 5 x + 6}{x - 3}

2 \leq x < 3 or x > 3

Interval Notation

[2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

2 \leq x < 3 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3 or x > 3

f (x) = csc (x^{2})

f (x) = \frac{2 x + 8}{x ^{2} + 6 x + 8}

f (x) = - \frac{4}{x}

f (x) = \frac{10}{x + 1}

f (x) = x^{\frac{2}{3}} (x - 4)

What is the domain of f(x)=sqrt((x^2-5x+6)/(x-3)) ?
The domain of f(x)=sqrt((x^2-5x+6)/(x-3)) is 2<= x<3\lor x>3