What is the domain of f(x)=sqrt((2-x)/(x^2-2x-3)) ?

The domain of f(x)=sqrt((2-x)/(x^2-2x-3)) is x<-1\lor 2<= x<3

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domain of f(x)=sqrt((2-x)/(x^2-2x-3))

domain

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

x < - 1 or 2 \leq x < 3

Interval Notation

Solution steps

Find non-negative values for radicals:

x < - 1 or 2 \leq x < 3

Find undefined (singularity) points:

x = 3, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 2 \leq x < 3

e^{x} - 2 x

f (x) = \frac{x - 1}{3 x - 5}

f (x) = - 8 x + 4

f (x) = \frac{t}{t ^{2} - 81}

\frac{x + 3}{x - 5}

What is the domain of f(x)=sqrt((2-x)/(x^2-2x-3)) ?
The domain of f(x)=sqrt((2-x)/(x^2-2x-3)) is x<-1\lor 2<= x<3