What is the domain of f(x)=((sqrt(4+x)))/(3-x) ?

The domain of f(x)=((sqrt(4+x)))/(3-x) is -4 3

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domain of f(x)=((sqrt(4+x)))/(3-x)

domain

f (x) = \frac{( 4 + x )}{3 - x}

- 4 \leq x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 4 \leq x < 3 or x > 3

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

(5, 4), (- 2, 1)

f (x) = \frac{7}{x - 2}

f (x) = 2

h (x) = - 4 x + 3

What is the domain of f(x)=((sqrt(4+x)))/(3-x) ?
The domain of f(x)=((sqrt(4+x)))/(3-x) is -4<= x<3\lor x>3