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Consider the function below. List the answers.

 

\(\displaystyle{f(x)=\frac{{x^{2}+11x+28}}{{x^{2}-16}}}\)

 

For what real numbers is the function not continuous?

 

For which of those is the discontinuity removable?

 Feb 23, 2022
edited by GAMEMASTERX40  Feb 23, 2022
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The function is not continuous when an x makes the denominator  = 0.....so.....

x^2 - 16   = 0

(x + 4) ( x - 4)  = 0

Setting each factor to 0  and solving for x  produces   x = -4  and  x = 4

 

Factor the   numerator  as  ( x + 4) ( x + 7)

 

We are left with

 

(x + 4) ( x + 7)             ( x + 7)

___________  =        _______       

(x + 4) ( x - 4)              ( x  - 4)

 

The discontinuity is  removable  at  ( x + 4)  = 0    ⇒  x = - 4

 

 

cool cool cool

 Feb 23, 2022

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