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anonymous

  • one year ago

Show that if f and g are even functions, then f+g and f times g are even.

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  1. freckles
    • one year ago
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    \[\text{ we are given } f(x)=f(-x) \text{ and } g(x)=g(-x) \\ \text{ \let's call the \sum of } f \text{ and } g , h \\ h(x)=f(x)+g(x) \] plug in -x

  2. freckles
    • one year ago
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    We are trying to see if h(x)=h(-x) and if so h is even

  3. anonymous
    • one year ago
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    so i can just show your way and it proves that its even??

  4. freckles
    • one year ago
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    if you show h(x)=h(-x) you are done

  5. freckles
    • one year ago
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    have you replace x with -x in h(x)=f(x)+g(x)

  6. freckles
    • one year ago
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    and then use that f(-x)=f(x) and g(-x)=g(x)?

  7. anonymous
    • one year ago
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    yes

  8. freckles
    • one year ago
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    ok you can try showing v(x)=f(x)*g(x) is also even replace x with -x again and use the fact that f and g are even to see if v(x)=v(-x)

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