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)
A) 0
B) 4
C) -4
D) 8
E) -8
f(4)=(4^2−16)/(4−4)
f(4)=0/0
you can't divide by zero. I don't understand the question.
You are correct; you cannot divide by zero. So, f(x) is not defined for x=4.
However, for any other value of x,
f(x) = (x-4)(x+4)/(x-4) = (x+4)
So, if you define f(4) = 8, then f(x) = x+4 for all values of x, and is now continuous.
So it is D?
yes, that would be correct.
To answer this question, we need to find the limit of the function as x approaches 4. The limit will provide us with the value that needs to be defined for f(4) in order to remove the discontinuity.
Let's start by factoring the numerator of the function: f(x) = (x^2 - 16) = (x + 4)(x - 4).
Now, let's substitute x = 4 into the factored form of the function: f(4) = (4 + 4)(4 - 4) = 8 * 0 = 0.
Since f(4) is equal to zero, we have found the value that needs to be defined for f(4) to remove the discontinuity. This corresponds to answer choice A) 0.
Thus, the correct answer is A) 0.