What is the domain of f(x)=(sqrt(x+3))/(1-x) ?

The domain of f(x)=(sqrt(x+3))/(1-x) is -3 1

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domain of f(x)=(sqrt(x+3))/(1-x)

domain

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

- 3 \leq x < 1 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- 3 \leq x < 1 or x > 1

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

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

x - 2 - x^{2}

f (x) = 2 x^{2} - 4 x + 8

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