What is the domain of f(x)=sqrt((x^2-5x+6)/(x+4)) ?

The domain of f(x)=sqrt((x^2-5x+6)/(x+4)) is -4 = 3

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domain of f(x)=sqrt((x^2-5x+6)/(x+4))

domain

f (x) = \frac{x ^{2} - 5 x + 6}{x + 4}

- 4 < x \leq 2 or x \geq 3

Interval Notation

(- 4, 2] \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

- 4 < x \leq 2 or x \geq 3

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

- 4 < x \leq 2 or x \geq 3

f (x) = \frac{1}{x ^{4} - 5 x ^{2} + 4}

\frac{1}{2 x}

f (x) = x - 4 + 1

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

f (x) = \frac{4 - x ^{2}}{2 x ^{2} - 7 x - 4}

What is the domain of f(x)=sqrt((x^2-5x+6)/(x+4)) ?
The domain of f(x)=sqrt((x^2-5x+6)/(x+4)) is -4<x<= 2\lor x>= 3