Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Find the domain of function f(x) = 2 log (10−x/10 +x). Determine whether the function is even or odd.

Sagot :

kate200468
[tex] f(x) = 2 log ( \frac{10-x}{10+x} )\\ \\D:\ \frac{10-x}{10+x}>0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \wedge\ \ \ \ \ \ \ \ \ \ \ \ 10+x \neq 0\\\\.\ \ \ \ \ (10-x)(10+x)>0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \neq 0\\\\.\ \ \ \ \ x\in (-10;10)\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=(-10;10)-\{0\}\\------------------------------ \\ [/tex]

[tex]the\ function\ is\ even\ \ \Leftrightarrow\ \ \ f(-x)=f(x)\ \ \ \wedge\ \ \ x,(-x)\in D\\\\the\ function\ is\ odd\ \ \ \Leftrightarrow\ \ \ f(-x)=-f(x)\ \ \ \wedge\ \ \ x,(-x)\in D\\-----------------------------\\\\f(-x)=2log( \frac{10-(-x)}{10+(-x)} )=2log( \frac{10+x}{10-x} )=2log( \frac{10-x}{10+x} )^{-1}=-2log( \frac{10-x}{10+x} )=\\ \\=-f(x)\ \ \ \ \Rightarrow\ \ \ the\ function\ is\ odd[/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.