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

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

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FUNCTION_MANY#domain of f(x)= x/(12-x-x^2)+sqrt((x+8)/2-5)

domain

f (x) = \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

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