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Consider the function below. List the answers.

 

\(\displaystyle{f(x)=\frac{{x^{2}-x-6}}{{x^{2}-3x-10}}}\)

 

For what real numbers is the function not continuous?

 

For which of those is the discontinuity removable?

 Feb 23, 2022
 #1
avatar+122390 
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Factor as   ( x -3) (x + 2)

                 ____________

                  ( x - 5) ( x + 2)

 

The function is not continuous at x values that make the denominator = 0   ⇒ x= 5  and x = -2

 

We have a removable discontinuity  at    x + 2 = 0  ⇒     x =  -2

 

 

cool cool cool

 Feb 23, 2022

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