Question

If f(x)=x^2-16/x 4 is continuous at x=-4, find f(-4)

Answer 1

The simplified form of the function f(x) is (x + 4), and after substituting x with -4, we find that f(-4) equals 0.

Step-by-step explanation:

If we want to check if the function f(x) = ⁡x^2 - 16/⁡x + 4 is continuous at x = -4 and find f(-4), we need to first simplify the expression if possible and then substitute x with -4.

Let's simplify the given function:

• ⁡f(x) = ⁡x^2 - 16/⁡x + 4

• ⁡f(x) = (⁡x - 4)(⁡x + 4)/⁡x + 4 (Factor the numerator)

• ⁡f(x) = (⁡x + 4) (since we can cancel the (⁡x - 4) term in the numerator with the ⁡x in the denominator)

Now that we have simplified the function, we substitute x with -4:

• ⁡f(-4) = (-4 + 4)

• ⁡f(-4) = 0

Therefore, f(-4) equals 0 when the function is continuous at x = -4.