1. Tardigrade
  2. Question
  3. Mathematics
  4. The function f(x) = 3x - 5 for x < 3 and - x + 1 for x > 3 and = c for x = 3 and is continuous at x = 3, if c is equal to

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Q. The function $f(x) = 3x - 5$ for $x < 3$ and $- x + 1$ for $x > 3 $ and = $c$ for $x$ = 3 and is continuous at $x$ = 3, if $c$ is equal to

Solution:

$\lim _{x\to 3-} f(x) = \lim _{x\to 3} (3x -5) = 9 - 5 = 4 $
$\lim _{x\to 3+} f(x) = \lim _{x\to 3} (x+1) = 3+ 1 = 4$
$\therefore $ $\lim _{x\to 3} f(x) = 4 = f(3) = c \, \therefore \, c= 4 $
[ $\because \, f$ is continuous at $x$ = 3]