Find the domain of the function.

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The discussion focuses on finding the domain of the real-valued function f(x) = (x - 10) / √(x² + 9x + 8). The quadratic expression x² + 9x + 8 is factored into (x + 8)(x + 1), which is a standard factoring technique. The domain of the function is determined by ensuring the expression under the square root is non-negative, leading to the conclusion that x must be greater than or equal to -8 and not equal to -1 to avoid division by zero.

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Find the domain of the real valued function:

f(x)=x−10−−−−−√x2+9x+8=x−10−−−−−√(x+8)(x+1)

Why does the x2+9x+8 become (x+8)(x+1)?

Thanks for the help!
 
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mitchconnor said:
Find the domain of the real valued function:

f(x)=x−10−−−−−√x2+9x+8=x−10−−−−−√(x+8)(x+1)

Why does the x2+9x+8 become (x+8)(x+1)?

Thanks for the help!

I'm not entirely sure what mathematical operation is occurring between the $x-10$ and the $\sqrt{x^{2}+9x+8}$. Could you please clarify that for me?

As for $x^{2}+9x+8=(x+8)(x+1)$, that is a straight-forward factoring problem. If you multiply the RHS out, you will get the LHS.
 

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