What is the domain of f(x)=(sqrt(3+x))/(5-x) ?

The domain of f(x)=(sqrt(3+x))/(5-x) is -3 5

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domain of f(x)=(sqrt(3+x))/(5-x)

domain

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

- 3 \leq x < 5 or x > 5

Interval Notation

[- 3, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 3 \leq x < 5 or x > 5

\frac{3 x ^{2} - 27}{x ^{2} + x - 6}

3 x^{2} + 5

f (x) = - 36 w^{2} + 240 w

\frac{- 2}{x + 2}

g (x) = (x + 6)^{2} + 16

What is the domain of f(x)=(sqrt(3+x))/(5-x) ?
The domain of f(x)=(sqrt(3+x))/(5-x) is -3<= x<5\lor x>5