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What is the domain of the real-valued function f(x) = (2x - 7)/sqrt(x^2 - 7x + 6)?

 Jul 19, 2022
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The denominator  cannot = 0

 

So   x^2  -7x +6 =  (x -6) (x - 1)     so  x cannot  be  1 , 6

 

Also  x^2 - 7x + 6  must be ≥  0

 

So

 

(x -1) (x -6) ≥  0

 

This  is true  whenever    x < 1     and  x > 6

 

So

 

The domain is   ( -inf , 1)  U ( 6  ,inf)

 

 

cool cool cool

 Jul 19, 2022

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