MHB Find the domain of the function.

  • Thread starter Thread starter mitchconnor
  • Start date Start date
  • Tags Tags
    Domain Function
AI Thread Summary
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.
mitchconnor
Messages
2
Reaction score
0
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!
 
Mathematics news on Phys.org
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

Similar threads

Replies
3
Views
1K
Replies
11
Views
2K
Replies
3
Views
1K
Replies
5
Views
1K
Replies
7
Views
3K
Replies
5
Views
1K
Back
Top