Question

I looked at a video about dividing by zero, but I dont understand this question. Couldnt x=-4 also be undefined?

Answer 1

x = -4 is not undefined because f(x) = x+4 is in the top part, the numerator, not the denominator. So the value that makes f(x) = x + 4 zero does not result in a division by zero.

Indeed, if we try to evaluate (f/g)(-4), then we get

  $\displaystyle\left( \frac{f}{g}\right)(-4) = \frac{f(-4)}{g(-4)} = \frac{-4+4}{-4-3} = \frac{0}{-7} = 0,$

which does not involve a division by zero.

However, attempting to evaluate (f/g)(3) leads us to

  $\displaystyle\left( \frac{f}{g}\right)(3) =\frac{3+4}{3-3} = \frac{7}{0},$

which involves a division by zero, and divisions by zero are undefined