QUESTION \( 10 \cdot 1 \) POINT Choose one point in the figure that is NOT in the domain of \( f(x)=\tan (x) \) defined in the interval \( -2 \pi \leq x \leq 2 \pi \)

To solve this problem, we need to identify the points within the interval \(-2\pi \leq x \leq 2\pi\) where the function \(f(x) = \tan(x)\) is undefined. The tangent function, \(\tan(x)\), is undefined at points where its argument, \(x\), is an odd multiple of \(\frac{\pi}{2}\). The general form of such points is \(x = \frac{(2n+1)\pi}{2}\), where \(n\) is an integer. Now, let's find the values of \(n\) that will give us points within the interval \(-2\pi \leq x \leq 2\pi\): 1. For \(n = -2\), \(x = \frac{(2(-2)+1)\pi}{2} = \frac{-4+1\pi}{2} = -\frac{3\pi}{2}\) 2. For \(n = -1\), \(x = \frac{(2(-1)+1)\pi}{2} = \frac{-2+1\pi}{2} = -\frac{\pi}{2}\) 3. For \(n = 0\), \(x = \frac{(2(0)+1)\pi}{2} = \frac{\pi}{2}\) 4. For \(n = 1\), \(x = \frac{(2(1)+1)\pi}{2} = \frac{3\pi}{2}\) All these points are within the interval \(-2\pi \leq x \leq 2\pi\). Therefore, the points that are NOT in the domain of \(f(x) = \tan(x)\) within this interval are: - \(x = -\frac{3\pi}{2}\) - \(x = -\frac{\pi}{2}\) - \(x = \frac{\pi}{2}\) - \(x = \frac{3\pi}{2}\) Choose one of these points as your answer. For example, you could choose \(x = \frac{\pi}{2}\) as the point that is NOT in the domain of \(f(x) = \tan(x)\) within the interval \(-2\pi \leq x \leq 2\pi\).