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  • 24-01-2022
  • Mathematics
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f(x) = 2x+5 if x<=1, -2x+1 if x>=-1 is continuous at x = -1. t or f

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LammettHash
LammettHash LammettHash
  • 24-01-2022

The given piecewise-defined function f(x),

[tex]f(x) = \begin{cases} 2x + 5 & \text{if } x \le -1 \\ -2x + 1 & \text{if } x \ge -1\end{cases}[/tex]

is continuous at x = -1 if both limits as x approaches -1 from either side are the same. We have

[tex]\displaystyle \lim_{x\to-1^-} f(x) = \lim_{x\to-1} (2x+5) = 3[/tex]

[tex]\displaystyle \lim_{x\to-1^+} f(x) = \lim_{x\to-1} (-2x+1) = 3[/tex]

so the claim is true, f(x) is indeed continuous at x = -1.

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