osanseviero
  • osanseviero
A function operation
Mathematics
jamiebookeater
  • jamiebookeater
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osanseviero
  • osanseviero
if \[F(x)=\frac{ 1 }{ x }\] find and express its simplest form: \[\frac{ f(a+h)-f(a) }{ h }\]
osanseviero
  • osanseviero
That's all I have, what should I do?
anonymous
  • anonymous
You should get -1/ (a(a+h))

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osanseviero
  • osanseviero
\[(\frac{ 1 }{ a+h }-\frac{ 1 }{ a }) \div h\]
osanseviero
  • osanseviero
Like that?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Yes, like that!
osanseviero
  • osanseviero
Can you explain how did you simplify, please?
anonymous
  • anonymous
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))
anonymous
  • anonymous
makes sense?
osanseviero
  • osanseviero
yep, thanks
anonymous
  • anonymous
welcome.
osanseviero
  • osanseviero
I had a silly math confusion

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