What is the domain of f(x)=(sqrt(1-x))/(x^2-4) ?

The domain of f(x)=(sqrt(1-x))/(x^2-4) is x<-2\lor-2<x<= 1

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domain of f(x)=(sqrt(1-x))/(x^2-4)

domain

f (x) = \frac{1 - x}{x ^{2} - 4}

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 = 2, x = - 2

Combine real regions and undefined points for final function domain

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

f (x) = 3 + \frac{2}{x}

f (x) = 3 x - 11

f (x) = \frac{x - 1}{x ^{2} + 4 x - 5}

y = \frac{x}{x + 4}

y = \frac{x}{x + 8}

What is the domain of f(x)=(sqrt(1-x))/(x^2-4) ?
The domain of f(x)=(sqrt(1-x))/(x^2-4) is x<-2\lor-2<x<= 1