anyecastro16 anyecastro16
  • 14-05-2019
  • Mathematics
contestada

What is the discontinuity of the function f(x)= x^2-4x-12/x+2

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 23-05-2019

Answer:

[tex]x=-2[/tex].

Step-by-step explanation:

The rational function given to us is:

[tex]f(x)=\frac{x^2-4x-12}{x+2}[/tex]

We can factor the numerator to obtain

[tex]f(x)=\frac{(x+2)(x-6)}{x+2}[/tex]

We can see clearly that, there is a linear common factor of both the numerator and the denominator.

This factor is [tex](x+2)[/tex].

This implies that, there is a removable discontinuity at [tex]x=-2[/tex].

Therefore, there is a removable discontinuity at [tex]x=-2[/tex].

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