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What is the domain of the function$$\ell(y) = \frac{1}{(y-2)+(y-8)}~?$$Express your answer in interval notation.

 Aug 3, 2022
 #1
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We need y not equal to 2, and y not equal to 8, so the domain is (-inf,2) U (2,8) U (8,inf).

 Aug 3, 2022
 #2
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The denominator simplifies to

 

2y -10

 

Since  this cannot = 0     then  y = 5   is NOT in the domain

 

So

 

domain  =   (-inf , 5) U ( 5 ,inf )

 

 

cool cool cool

 Aug 3, 2022

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