anonymous
  • anonymous
f(x)= {2x-3, x cannot equal 2 and 0, x=2} has a removable discontinuity. Redefine f(x) so that it is continuous at x=2.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
replace \(x\) by \(2\) and see what you get
anonymous
  • anonymous
or better yet, just remove all the verbiage and write \[f(x)=2x-3\]
anonymous
  • anonymous
I got 1?

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anonymous
  • anonymous
yeah ignore my first answer, just make \(f(x)=2x-3\) for all \(x\) then it is continuous for sure it is a line
anonymous
  • anonymous
what about the 0?
anonymous
  • anonymous
what about it?
anonymous
  • anonymous
its the answer just f(x)=2x−3 ?
anonymous
  • anonymous
\[f(x) = \left\{\begin{array}{rcc} 2x-3 & \text{if} & x \neq 2 \\ 0& \text{if} & x =2 \end{array} \right. \]
anonymous
  • anonymous
the only reason this is not continuous at \(2\) is because \(2\times 2-3=-1\) and this function is defined so that \(f(2)=0\) rather than \(-1\) for some reason to get rid of that stupid discontinuity, make the function just \(f(x)=2x-3\) for all \(x\) like normal, and then it is continuous
anonymous
  • anonymous
oh okay thank you so much:)
anonymous
  • anonymous
can i ask you another question

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