What value must be defined for f(4) to remove the discontinuity of this function at x = 4?
f(x)= x^2-16/x-4
0
4
-4
8
-8
for x ≠ 4, f(x) = x+4
so, f(4) = 8 to fill in the removable discontinuity.
To remove the discontinuity of the function at x = 4, we need to find the value of f(4) that makes the function continuous at that point.
Let's analyze the function and its behavior around x = 4.
The given function is f(x) = (x^2 - 16)/(x - 4).
At x = 4, the function has a discontinuity because the denominator becomes zero, which is not defined. Therefore, we have an "undefined" point at x = 4.
To remove this discontinuity, we need to find a value of f(4) that makes the function defined at x = 4. In other words, we need to find the limit of f(x) as x approaches 4 from both sides.
To find the limit, we can simplify the function by factoring the numerator:
f(x) = (x - 4)(x + 4)/(x - 4)
= (x + 4)
Now we can evaluate the limit as x approaches 4:
lim(x->4) f(x) = lim(x->4) (x + 4) = 4 + 4 = 8
Therefore, to remove the discontinuity at x = 4, we need to define f(4) = 8.