What is the domain of g(x)=(sqrt(4+x))/(1-x) ?

The domain of g(x)=(sqrt(4+x))/(1-x) is -4 1

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domain of g(x)=(sqrt(4+x))/(1-x)

domain

g (x) = \frac{4 + x}{1 - x}

- 4 \leq x < 1 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- 4 \leq x < 1 or x > 1

f (x) = \frac{1}{x ^{2} + 25}

4 + x - 2

\frac{1}{( x - 1 ) ^{2}}

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

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

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