OpenStudy9
  • OpenStudy9
Is y=(x^3)+1 and Even or Odd Function???
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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FibonacciChick666
  • FibonacciChick666
Can you tell me what it means for something to be even or odd?
FibonacciChick666
  • FibonacciChick666
What are the definitions of each term?
OpenStudy9
  • OpenStudy9
Well, if a function is Even, than the negative of it is the same as the positive of it. If it is Odd, than \[-f(x)=f(-x)\]

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OpenStudy9
  • OpenStudy9
Is it Odd??
FibonacciChick666
  • FibonacciChick666
Good on definition, now, pick a convenient number, say x=1 and see which definition holds
OpenStudy9
  • OpenStudy9
1^3 +1 is 2. (-1)^3 +1= 0 so not even, 1^3 +1 is 2, and -(1^3 +1) is -2. So the Answer is Neither!?
FibonacciChick666
  • FibonacciChick666
yep yep :)
OpenStudy9
  • OpenStudy9
Thanks!!!
FibonacciChick666
  • FibonacciChick666
You just proved that it is not odd and that it is not even.
FibonacciChick666
  • FibonacciChick666
now, if it was only x^3 it would be a different story. you would find that it is odd. So if it is asking if the mother function is even or odd, it would be odd.
OpenStudy9
  • OpenStudy9
Oh, I see! THank YOU
FibonacciChick666
  • FibonacciChick666
wait hold on a sec. One issue
FibonacciChick666
  • FibonacciChick666
I missed something in your work
FibonacciChick666
  • FibonacciChick666
I skimmed sorry. so here: "1^3 +1 is 2. (-1)^3 +1= 0 so not even, 1^3 +1 is 2, and \[\color\red{-(1^3 +1)}\] is -2. So the Answer is Neither!?" What is marked in red, isn't actually f(-x). f(-x) is (-1)^3+1 when f(x) is 1^3+1
OpenStudy9
  • OpenStudy9
OK

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