What is the domain of f(x)=(sqrt(1+x))/(x^2-2x-8) ?

The domain of f(x)=(sqrt(1+x))/(x^2-2x-8) is -1 4

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domain of f(x)=(sqrt(1+x))/(x^2-2x-8)

domain

f (x) = \frac{1 + x}{x ^{2} - 2 x - 8}

- 1 \leq x < 4 or x > 4

Interval Notation

[- 1, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 1

Find undefined (singularity) points:

x = 4, x = - 2

Combine real regions and undefined points for final function domain

- 1 \leq x < 4 or x > 4

What is the domain of f(x)=(sqrt(1+x))/(x^2-2x-8) ?
The domain of f(x)=(sqrt(1+x))/(x^2-2x-8) is -1<= x<4\lor x>4