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

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

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domain of f(x)=sqrt((2-x)/(x^2-9))

domain

f (x) = \frac{2 - x}{x ^{2} - 9}

x < - 3 or 2 \leq x < 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < - 3 or 2 \leq x < 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or 2 \leq x < 3

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

f (x) = - 13 x + 1

y = 3 x^{2} - 4 x - 1

f (x) = 2 (3)^{2} - 8 (3) + 2

1 - 3

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