What is the domain of f(x)=(sqrt(1-x))/(x^2-x-6) ?

The domain of f(x)=(sqrt(1-x))/(x^2-x-6) is x<-2\lor-2<x<= 1

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domain of f(x)=(sqrt(1-x))/(x^2-x-6)

domain

f (x) = \frac{1 - x}{x ^{2} - x - 6}

x < - 2 or - 2 < x \leq 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = 3, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x \leq 1

f (x) = (x - 2)^{5} + 3

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

(1, 2), (6, 1)

\frac{x}{x ^{2}}

7 x - 3

What is the domain of f(x)=(sqrt(1-x))/(x^2-x-6) ?
The domain of f(x)=(sqrt(1-x))/(x^2-x-6) is x<-2\lor-2<x<= 1