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What real values of x are not in the domain of $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x - 10|}$?

 Apr 6, 2022
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The denominator  cannot  =  0

 

Note that   l x^2 + 3x + 4  l   =  l (x -1) ( x + 4) l

And   l x^2 + 9x -10 l =  l (x -1) ( x + 10) l

 

So  we have

 

l (x -1) ( x + 4) l +  l (x -1) ( x + 10 l  =

 

( l x - 1 l  )  (  l (x + 4) l + l x + 10 l )

 

The only value of x that makes  this 0   is when x   = 1

 

So .....x =1   is not in the  domain

 

 

cool cool cool

 Apr 6, 2022

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