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

Answer:

Step-by-step explanation:

Given that

$f(x) = \frac{x^2-16}{6x-24}$

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

$\frac{x^2-16}{6x-24} =\frac{(x+4)(x-4)}{6(x-4)} \\=\frac{x+4}{6}$

If f(4) is defined as

$\frac{4+4}{6} =\frac{4}{3}$

then f becoms continuous at x=4 also