anonymous
  • anonymous
evaluate the difference quotient for the given function f(x)= 1/x, f(x)-f(a)/x-a
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[f(x)= 1/x\]\[f(a) = 1/2\] \[\frac{f(x)-f(a)}{x-a} =\frac{\frac 1x -\frac 1a}{x-a} \]
anonymous
  • anonymous
You have to simplify it more.
anonymous
  • anonymous
What do I do next?

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anonymous
  • anonymous
First simplify the numerator: \[ \frac 1 x - \frac 1 a = ? \]
anonymous
  • anonymous
\[ \frac 1x - \frac 1a = \frac a{xa}-\frac x{xa} = \frac{a-x}{xa} \]
anonymous
  • anonymous
So we have \[\large \frac{\frac{a-x}{xa}}{x-a} = \frac{a-x}{(xa)(x-a)} \]
anonymous
  • anonymous
and so the x-a and a-x cancels out?
anonymous
  • anonymous
Yeah, they cancel out to \(-1\).
anonymous
  • anonymous
Assuming that \(x\neq a\)
anonymous
  • anonymous
thank you!

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