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osanseviero

  • 2 years ago

A function operation

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  1. osanseviero
    • 2 years ago
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    if \[F(x)=\frac{ 1 }{ x }\] find and express its simplest form: \[\frac{ f(a+h)-f(a) }{ h }\]

  2. osanseviero
    • 2 years ago
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    That's all I have, what should I do?

  3. Easyaspi314
    • 2 years ago
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    You should get -1/ (a(a+h))

  4. osanseviero
    • 2 years ago
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    \[(\frac{ 1 }{ a+h }-\frac{ 1 }{ a }) \div h\]

  5. osanseviero
    • 2 years ago
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    Like that?

  6. Easyaspi314
    • 2 years ago
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    I'll start you off.......... Given: f(x) = 1/x So, f(a+h) = 1/(a+h) and f(a) = 1/a So the expression you typed above is just: [ (1/(a+h) - 1/a] /h When you simplify that complex fraction above (not hard at all), you get -1/[a(a+h)] as your final answer.

  7. Easyaspi314
    • 2 years ago
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    Yes, like that!

  8. osanseviero
    • 2 years ago
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    Can you explain how did you simplify, please?

  9. Easyaspi314
    • 2 years ago
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    Let's take the numerator........ 1/(a+h) - 1/a To subtract, you get the LCD which is a(a+h), so 1/(a+h) - 1/a = [a-(a+h)]/a(a+h) = -h/(a(a+h)) Now, the denominator is just h, so you get -h/(a(a+h)) divided by h/1 = -1/(a(a+h))

  10. Easyaspi314
    • 2 years ago
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    makes sense?

  11. osanseviero
    • 2 years ago
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    yep, thanks

  12. Easyaspi314
    • 2 years ago
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    welcome.

  13. osanseviero
    • 2 years ago
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    I had a silly math confusion

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