Đáp án:
a. \(\left[ \begin{array}{l}
x = \dfrac{\pi }{3} + k2\pi \\
x = - \dfrac{\pi }{3} + k2\pi
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
C6:\\
a.f\left( x \right) = 0\\
\to 2\cos x - 1 = 0\\
\to \cos x = \dfrac{1}{2}\\
\to \left[ \begin{array}{l}
x = \dfrac{\pi }{3} + k2\pi \\
x = - \dfrac{\pi }{3} + k2\pi
\end{array} \right.\left( {k \in Z} \right)\\
b.Do: - 1 \le \cos x \le 1\\
\to - 2 \le 2\cos x \le 2\\
\to - 2 - 1 \le 2\cos x - 1 \le 2 - 1\\
\to - 3 \le f\left( x \right) \le 1\\
\to Max = 1 \Leftrightarrow \cos x = 1 \Leftrightarrow x = k2\pi \\
Min = - 3 \Leftrightarrow \cos x = - 1 \Leftrightarrow x = \pi + k2\pi \left( {k \in Z} \right)
\end{array}\)
