Question

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.

Answer 1

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.

Answer 2

So it is D?

Answer 3

yes, that would be correct.