Questions: Let f(x) = cos^(-1)(cos(x)), which is valid for all x. Sketch the graph of this periodic function f. Find its period and the range of its values f(x).

Let f(x) = cos^(-1)(cos(x)), which is valid for all x. Sketch the graph of this periodic function f. Find its period and the range of its values f(x).
Transcript text: Let $f(x) = \cos^{-1}(\cos(x))$, which is valid for all x. Sketch the graph of this periodic function f. Find its period and the range of its values f(x).
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Solution

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Solution Steps

Step 1: Define the function

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

Step 2: Determine the period

The function \( \cos^{-1}(\cos(x)) \) is periodic with a period of \( 2\pi \).

Step 3: Determine the range

The range of \( f(x) = \cos^{-1}(\cos(x)) \) is \( [0, \pi] \).

Final Answer

The period of the function is \( 2\pi \) and the range is \( [0, \pi] \).

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