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

The domain of f(x)=(sqrt(x))/(x^2-5x+6) is 0 3

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

domain

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

0 \leq x < 2 or 2 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 3, x = 2

Combine real regions and undefined points for final function domain

0 \leq x < 2 or 2 < x < 3 or x > 3

What is the domain of f(x)=(sqrt(x))/(x^2-5x+6) ?
The domain of f(x)=(sqrt(x))/(x^2-5x+6) is 0<= x<2\lor 2<x<3\lor x>3