What is the domain of x/(12-x-x^2)+sqrt((x+8)/2-5) ?

The domain of x/(12-x-x^2)+sqrt((x+8)/2-5) is 2 3

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domain of x/(12-x-x^2)+sqrt((x+8)/2-5)

domain

\frac{x}{12 - x - x ^{2}} + \frac{x + 8}{2} - 5

2 \leq x < 3 or x > 3

Interval Notation

[2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = - 4, x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3 or x > 3

- x - 1

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

y = \frac{5 - x}{lo g _{10} ( x )}

f (x) = \frac{2 x - 7}{x - 3}

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

What is the domain of x/(12-x-x^2)+sqrt((x+8)/2-5) ?
The domain of x/(12-x-x^2)+sqrt((x+8)/2-5) is 2<= x<3\lor x>3