Question

For what values does the function fail to exist?

f(x)= x/x³-16x²
A. x=0 and x=16
B. x=0 and x=-16
C. x=-4 and x=0 and x=4
D. x=0 and x=4

Answer 1

The function f(x) = x/(x³ - 16x²) fails to exist at x = 0 and x = 16, where the denominator equals zero, making division by zero impossible. The correct answer is A. x=0 and x=16.

Step-by-step explanation:

The question asks for the values at which the function f(x) = x/(x³ - 16x²) fails to exist. To find these values, we need to identify for which values of x the denominator becomes zero, as division by zero is undefined and the function cannot exist at those points.

We must first factor out the common term in the denominator, which gives us x(x² - 16x). We can then set the denominator equal to zero and solve for x: x(x - 16) = 0. This yields two possible values: x = 0 and x = 16.

Therefore, the function fails to exist at x = 0 and x = 16, since at these points, the denominator becomes zero, creating a situation where you're dividing by zero.