Answer:
f(x) = (x+2)(x-8)/(x-6)(x+4) <-> x=6,x=-4
i(x) = (x-4)(x-6)/(x-2)(x+8) <-> x=2,x=-8
k(x) = (x-2)(x+8)/(x+6)(x-4) <-> x=-6,x=4
m(x) = (x+4)(x-6)/(x+2)(x-8) <-> x=-2,x=8
Step-by-step explanation:
The function is discontinuous if the denominator is zero.
We will check for which function the values are given
1) f(x) = (x+2)(x-8)/(x-6)(x+4)
if x = 6 and x = -4 the denominator is zero
So, x=6 and x=-4 given
2) g(x) = (x+4)(x-8)/(x+2)(x-6)
if x = -2 and x = 6 the denominator is zero
So, x= -2 and x= 6 not given so, g(x) will not be considered
3) h(x)= (x+2)(x-6)/(x-8)(x+4)
if x = 8 and x = -4 the denominator is zero
So, x= 8 and x= -4 not given so, h(x) will not be considered
4) i(x) = (x-4)(x-6)/(x-2)(x+8)
if x = 2 and x = -8 the denominator is zero
So, x= 2 and x= -8 given
5) j(x) = (x-2)(x+6)/(x-4)(x+8)
if x = 4 and x = -8 the denominator is zero
So, x= 4 and x= -8 not given so, j(x) will not be considered
6) k(x) = (x-2)(x+8)/(x+6)(x-4)
if x = -6 and x = 4 the denominator is zero
So, x= -6 and x= 4 given
7) l(x) = (x-4)(x+8)/(x+6)(x-2)
if x = -6 and x = 2 the denominator is zero
So, x= -6 and x= 2 not given so, l(x) will not be considered
8) m(x) = (x+4)(x-6)/(x+2)(x-8)
if x = -2 and x = 8 the denominator is zero
So, x= -2 and x= 8 given
