Question

Find the domain of the function f/g(x) given f(x)=x^2+2x-8 and g(x)=x^2-16

Answer 1

The domain of the function f/g(x) is all real numbers except x = 4 and x = -4, because these are the values for which the denominator g(x) is zero. The domain in interval notation is (-∞, -4) ∪ (-4, 4) ∪ (4, +∞).

Step-by-step explanation:

To find the domain of the function f/g(x) given f(x)=x^2+2x-8 and g(x)=x^2-16, we need to determine the set of all possible x-values for which this function is defined. The function f/g(x) is not defined when the denominator g(x) is equal to zero, because division by zero is undefined in mathematics.

First, set the denominator equal to zero and solve for x:

• g(x) = x^2 - 16 = 0
• x^2 = 16
• x = ±4

Therefore, the denominator is equal to zero when x = 4 or x = -4. These values should be excluded from the domain.

Thus, the domain of the function f/g(x) is all real numbers except x = 4 and x = -4. In interval notation, the domain is (-∞, -4) ∪ (-4, 4) ∪ (4, +∞).

Answer 2

C)
`\x`

Step-by-step explanation:

`(x^2+2x-8)/(x^2-16)\\ \\((x+4)(x-2))/((x+4)(x-4))\\ \\x\\eq-4 \:or \:4`

Here,
`x\\eq-4` is a hole on the graph since
`x+4` exists in both the numerator and denominator.