What is the domain of f(x)=sqrt((7-x)/(x^2-x-2)) ?

The domain of f(x)=sqrt((7-x)/(x^2-x-2)) is x<-1\lor 2<x<= 7

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domain of f(x)=sqrt((7-x)/(x^2-x-2))

domain

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

x < - 1 or 2 < x \leq 7

Interval Notation

(- \infty, - 1) \cup (2, 7]

Solution steps

Find non-negative values for radicals:

x < - 1 or 2 < x \leq 7

Find undefined (singularity) points:

x = 2, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 2 < x \leq 7

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

f (x) = 2 x - 3 + 5

\frac{x + 10}{x - 5}

6 x^{2} + 500 x + 8000

f (x) = arccos (e^{3 x})

What is the domain of f(x)=sqrt((7-x)/(x^2-x-2)) ?
The domain of f(x)=sqrt((7-x)/(x^2-x-2)) is x<-1\lor 2<x<= 7