anonymous
  • anonymous
Let f(x) = {1-x, if x<=-1 {SQRT (x+b), if x>-1 Determine the value of b that makes f(x) continuous at x=-1.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\(f\) is continuous at -1 if \[\lim_{x\to-1^-}f(x)=\lim_{x\to-1^+}f(x)\] and these limits are equal to \(f(-1)\).
anonymous
  • anonymous
\[\lim_{x\to-1^-}f(x)=\lim_{x\to-1^-}(1-x)=1-(-1)=2\] \[\lim_{x\to-1^+}f(x)=\lim_{x\to-1^+}\sqrt{x+b}=\sqrt{b-1}\] By the definition of \(f\), you have \(f(-1)=2\), so the function is continuous at -1 if \[\sqrt{b-1}=2\]
anonymous
  • anonymous
that's what I initially thought but pluged itin to the online course and it didn't work

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anonymous
  • anonymous
You got \(b=5\), right?
anonymous
  • anonymous
now I now thanks for the help
anonymous
  • anonymous
yw

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