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mitchelsewbaran Group Title

Give an example of an even function and explain algebraically why it is even.

  • one year ago
  • one year ago

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  1. ParthKohli Group Title
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    So, an even function \(f\) is a function where for all \(x\), \(f(x) = f(-x)\). The square function and the absolute-value functions are pretty cool examples.

    • one year ago
  2. mitchelsewbaran Group Title
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    is that it?

    • one year ago
  3. ParthKohli Group Title
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    Maybe.

    • one year ago
  4. ParthKohli Group Title
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    Do you know what \(|x|\) is?

    • one year ago
  5. mitchelsewbaran Group Title
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    x

    • one year ago
  6. ParthKohli Group Title
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    And \(|-x|\).

    • one year ago
  7. mitchelsewbaran Group Title
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    x

    • one year ago
  8. ParthKohli Group Title
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    Bang on!

    • one year ago
  9. ParthKohli Group Title
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    And do you know what \((-x)^2\) is?

    • one year ago
  10. mitchelsewbaran Group Title
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    x?

    • one year ago
  11. ParthKohli Group Title
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    Nope

    • one year ago
  12. mitchelsewbaran Group Title
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    o

    • one year ago
  13. mitchelsewbaran Group Title
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    x^2

    • one year ago
  14. ParthKohli Group Title
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    Yes.

    • one year ago
  15. ParthKohli Group Title
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    That's correct! =)

    • one year ago
  16. mitchelsewbaran Group Title
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    so how does that answer this question, bro? :)

    • one year ago
  17. ParthKohli Group Title
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    You just answered the question, “explain algebraically why it is even”. Look back at the definition.

    • one year ago
  18. hba Group Title
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    If f(-a)=f(a) then it is even example f(x)=x^2 f(-x)=(-x)^2 f(-x)=x^2 therfore, f(x)=f(-x) @parth explained it well :)

    • one year ago
  19. hba Group Title
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    @ParthKohli *

    • one year ago
  20. ParthKohli Group Title
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    :)

    • one year ago
  21. ParthKohli Group Title
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    Let me do that for an absolute-value function too! So we define the absolute value function as follows\[f(x) = \cases{x \ \ \text{iff} \ \ x >0 \\ -x \ \ \text{iff} \ \ x < 0 }\]It is clear that \(f(-x)=f(x)=x\), hence an even function.

    • one year ago
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