Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Given
[tex]f(x)=-f(x)[/tex]We can sum f(x) on both sides, and we will get
[tex]f(x)+f(x)=-f(x)+f(x)_{}[/tex]But -f(x) + f(x) = 0, then
[tex]f(x)+f(x)=0[/tex]Now we can combine the terms and we get
[tex]2\cdot f(x)=0[/tex]Divide both sides by 2
[tex]f(x)=0[/tex]
And here we have solved our problem. That's the only function that is odd and even at the same time, the graph of this function is basically the x-axis because it's a constant in y = 0, we can see even and odd because
[tex]f(x)=0,\forall x\in\R[/tex]Therefore
[tex]\begin{gathered} f(x)=0=f(-x) \\ \\ f(x)=0=-f(x) \end{gathered}[/tex]Odd and even at the same time.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
