Question

Determine if the following function is continous at the point where x = -5.

f(x)=a.{ (x-5)/(x^2-25) x is not equal to -5, b.{-10 x=-5

Answer 1

The letter a{ is (x-5)/((x+5)(x-5)= (x+5) what happens next?
letter b is have no X so it stays the same

Answer 2

NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!

Answer 3

what?

Answer 4

???

Answer 5

x^2-25 factors to (x-5)(x+5)

Answer 6

so

(x-5)/(x^2-25)

(x-5)/((x-5)(x+5))

1/(x+5)

when x = -5, the denominator is x+5 = -5+5 = 0...but you cannot divide by zero

So x = -5 is not allowed in the domain causing a point of discontinuity here.