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Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2-5x+6-x^2}}$

 Aug 18, 2023
 #1
avatar+128393 
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The denominator  simplifies  to   sqrt  [ 6 - 5x  ]

 

Since  we  can't  take  the  sqrt  of   a negative and  the  denominator  must not = 0  we have that

 

6 - 5x  >   0

 

6 >  5x

 

(6/5) > x     or

 

x <  (6/5)

 

Domain =  ( -inf, 6/5)

 

 

cool cool cool

 Aug 18, 2023

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