First slide

Functions (XII)

Question

If f(x) is areal-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 tine $x = \frac{π}{2}$
D

symmetric about the origin

Solution

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

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