First slide

Continuity

Question

$The function f (x) = \cos^{- 1} (\cos x) is$

Moderate

A

$continuous at x = π$
B

$Discontinuous at x = π$
C

$Discontinuous at x = - π$
D

$f (x) = x \forall x \in R$

Solution

$f (x) = \cos^{- 1} (\cos x) = \{\begin{cases} 2 π + x for - 2 π < x < - π \\ - x for - π \leq x < 0 \\ x for 0 \leq x \leq π \\ 2 π - x for π < x < 2 π \end{cases}$
$f (x) is continuous at x = π, - π$

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