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mitchelsewbaran

  • 3 years ago

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

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  1. ParthKohli
    • 3 years ago
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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.

  2. mitchelsewbaran
    • 3 years ago
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    is that it?

  3. ParthKohli
    • 3 years ago
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    Maybe.

  4. ParthKohli
    • 3 years ago
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    Do you know what \(|x|\) is?

  5. mitchelsewbaran
    • 3 years ago
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    x

  6. ParthKohli
    • 3 years ago
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    And \(|-x|\).

  7. mitchelsewbaran
    • 3 years ago
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    x

  8. ParthKohli
    • 3 years ago
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    Bang on!

  9. ParthKohli
    • 3 years ago
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    And do you know what \((-x)^2\) is?

  10. mitchelsewbaran
    • 3 years ago
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    x?

  11. ParthKohli
    • 3 years ago
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    Nope

  12. mitchelsewbaran
    • 3 years ago
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    o

  13. mitchelsewbaran
    • 3 years ago
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    x^2

  14. ParthKohli
    • 3 years ago
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    Yes.

  15. ParthKohli
    • 3 years ago
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    That's correct! =)

  16. mitchelsewbaran
    • 3 years ago
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    so how does that answer this question, bro? :)

  17. ParthKohli
    • 3 years ago
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    You just answered the question, “explain algebraically why it is even”. Look back at the definition.

  18. hba
    • 3 years ago
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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 :)

  19. hba
    • 3 years ago
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    @ParthKohli *

  20. ParthKohli
    • 3 years ago
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    :)

  21. ParthKohli
    • 3 years ago
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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.

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