What is the domain of f(x)= 1/(sqrt(|x^2-5x+6|)) ?

The domain of f(x)= 1/(sqrt(|x^2-5x+6|)) is x 3

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domain of f(x)= 1/(sqrt(|x^2-5x+6|))

domain

f (x) = \frac{1}{∣ x ^{2} - 5 x + 6 ∣}

x < 2 or 2 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

Find undefined (singularity) points:

x = 2, x = 3

Combine real regions and undefined points for final function domain

x < 2 or 2 < x < 3 or x > 3

f (x) = \frac{1}{2 x + 4}

\frac{2 x ^{2} + 10 x + 12}{x ^{2} + 2 x - 3}

- \frac{1}{( x - 5 ) ^{4}}

y = 1

What is the domain of f(x)= 1/(sqrt(|x^2-5x+6|)) ?
The domain of f(x)= 1/(sqrt(|x^2-5x+6|)) is x<2\lor 2<x<3\lor x>3