MHB Find the domain of the function.

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The discussion centers on finding the domain of the function f(x) = (x - 10) / √(x² + 9x + 8), with a focus on the factorization of x² + 9x + 8 into (x + 8)(x + 1). Participants clarify that this factorization is a straightforward algebraic operation. The domain of the function is determined by the values of x that do not make the denominator zero or result in a negative value under the square root. Understanding the factorization helps in identifying the critical points that affect the domain. The conversation emphasizes the importance of proper algebraic manipulation in determining function properties.
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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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