What is the domain of f(x)= 1/(x-2)+sqrt(x+4) ?

The domain of f(x)= 1/(x-2)+sqrt(x+4) is -4 2

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domain of f(x)= 1/(x-2)+sqrt(x+4)

domain

f (x) = \frac{1}{x - 2} + x + 4

- 4 \leq x < 2 or x > 2

Interval Notation

[- 4, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- 4 \leq x < 2 or x > 2

f (x) = - 2 x^{3} + 6 x^{2} + 12

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

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

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

8 x^{2} - 48 x

What is the domain of f(x)= 1/(x-2)+sqrt(x+4) ?
The domain of f(x)= 1/(x-2)+sqrt(x+4) is -4<= x<2\lor x>2