For the function f, how would you remove the discontinuity? In other words, how would you define f(4) in order for f to be continuous at 4? Equation: f(x) = (x^2 − x − 12)/(x − 4)

Answer 1

f(x) = (x^2 -x -12)/(x-4) = (x-4)(x+3)/(x-4) = x+3

to remove the discontinuity

let f(x) = x+3

then

f(4) = 4+3 = 7

or

f(x) = (x^2 -x -12)/(x-4) when x does not equal 4

and f(x) = x+3 when x = 4

f(4) = 4+3 = 7

Answer 2

f(x) = x + 3 if x ≠ 4 and f(4) = 4 + 3 = 7