+0  
 
-1
23
2
avatar+1414 

Find the real numbers $x$ that are not in the domain of
\[f(x)=\frac{1}{(x^2-6x+8)-(x^2+x-6)}.\]

 Aug 20, 2023
 #2
avatar+177 
0

\(f(x)\) is a rational function, so an x-value that could realistically not be in the domain occurs when the denominator equals 0.

 

\((x^2 - 6x + 8) - (x^2 + x - 6) = 0 \\ x^2 - 6x + 8 - x^2 - x + 6 = 0 \\ -7x+14 = 0 \\ -7x = -14 \\ x = -2\)

 

The value of x = -2 causes the denominator to be 0, x = -2 is the only x-value not in the domain of this function!

 Aug 21, 2023

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