Question

For what values does the function fail to exist?

f(x) =x-7/ (x² - 4)(x+6)
A. X=-6, X = -2, and x = 2
B. x= -6, x= -2
C. X= -2, x=2, and x = 6
D. x= -2, x= 2

Answer 1

The function f(x) fails to exist for x = 2, x = -2, and x = -6, as these values make the denominator equal to zero.

Step-by-step explanation:

To determine for what values the function f(x) = \frac{x-7}{(x^2 - 4)(x+6)} fails to exist, we need to identify the values of x that make the denominator equal to zero.

These are the values that will create a division by zero scenario, which is undefined in mathematics. The denominator factors as (x - 2)(x + 2)(x + 6). Therefore, the values of x that make this expression zero are x = 2, x = -2, and x = -6.