First slide

Functions (XII)

Question

$If f (x) is a real-valued function defined as f (x) =$ $\ln (1 - \sin x), then the graph of f (x) is$

Moderate

A

$symmetric about the line x = π$
B

$symmetric about the y -axis$
C

$symmetric about the line x = \frac{π}{2}$
D

$symmetric about the origin$

Solution

$f (\frac{π}{2} - x) = \ln (1 - \cos x) and f (\frac{π}{2} + x) = \ln (1 - \cos x)$
$Thus, f (\frac{π}{2} + x) = f (\frac{π}{2} - x)$
$Thus, f (x) is symmetrical about line x = \frac{π}{2} .$

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