Find the domain of the following function and give your answer in interval notation

Question

F(x)=root x/x^2+7x+12

Answer 1

To determine the domain of the function F(x) = √(x)/(x^2 + 7x + 12), we need to find the values of x that make the function undefined.

First, let's consider the denominator x^2 + 7x + 12. Since dividing by zero is undefined, we need to find the values of x that make the denominator equal to zero.

Factorizing the denominator:
x^2 + 7x + 12 = (x + 3)(x + 4)

Setting each factor equal to zero:
x + 3 = 0 --> x = -3
x + 4 = 0 --> x = -4

Therefore, the function F(x) is undefined when x = -3 or x = -4, as these values would make the denominator zero.

The domain of the function F(x) is all real numbers except -3 and -4. In interval notation, this can be expressed as:
(-∞, -4) U (-4, -3) U (-3, ∞)