What is the domain of sqrt((4-x)/(x^2-9)) ?

The domain of sqrt((4-x)/(x^2-9)) is x<-3\lor 3<x<= 4

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domain of sqrt((4-x)/(x^2-9))

domain

\frac{4 - x}{x ^{2} - 9}

x < - 3 or 3 < x \leq 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < - 3 or 3 < x \leq 4

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or 3 < x \leq 4

x^{4} - 5 x^{3} 9 x^{2}

f (x) = x - 12 x + 35

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

f (x) = lo g_{10} (1 + 2 x)

\frac{6}{x} \cdot x - 7

What is the domain of sqrt((4-x)/(x^2-9)) ?
The domain of sqrt((4-x)/(x^2-9)) is x<-3\lor 3<x<= 4