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

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

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

domain

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

- 4 \leq x < 2 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 4 \leq x < 2 or x > 3

Find undefined (singularity) points:

x = 3, x = 2

Combine real regions and undefined points for final function domain

- 4 \leq x < 2 or x > 3

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

6 x - 1

x^{2} + 3 x + 2

f (x) = x^{3} - 3 x^{2}

arccot (x)

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