What is the domain of f(x)=(sqrt(4+x))/(5-x) ?

The domain of f(x)=(sqrt(4+x))/(5-x) is -4 5

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domain of f(x)=(sqrt(4+x))/(5-x)

domain

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

- 4 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 4 \leq x < 5 or x > 5

f (x) = \frac{( 8 x - 1 )}{2 x + 5}

f (x) = \frac{2 x + 3}{1 - 5 x}

5 x - 3 y = - 15

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

f (x) = 7^{x} + 4

What is the domain of f(x)=(sqrt(4+x))/(5-x) ?
The domain of f(x)=(sqrt(4+x))/(5-x) is -4<= x<5\lor x>5