Question

what are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 6x minus 24?

Answer 1

f(x) is discontinuous when 6x - 24 = 0
6x = 24
x = 4

Answer 2

Explanation:

Given that

`f(x) = (x^2-16)/(6x-24)`

WE have to find the discontinuities of the function.

The denominator 6x-24 becomes 0 when

x=4

Thus when x=4 then function becomes undefined.

Thus there is a discontinuity at x=4

But this discontinuity can be removed because

we have x=4 in the numerator

`(x^2-16)/(6x-24) =((x+4)(x-4))/(6(x-4)) \\=(x+4)/(6)`

If f(4) is defined as

`(4+4)/(6) =(4)/(3)`

then f becoms continuous at x=4 also