1. The problem is to evaluate the function $f(x) = e^{i\pi}$.\n\n2. We use Euler's formula, which states that for any real number $\theta$, $$e^{i\theta} = \cos(\theta) + i\sin(\theta).$$\n\n3. Applying this to $\theta = \pi$, we get $$e^{i\pi} = \cos(\pi) + i\sin(\pi).$$\n\n4. We know that $\cos(\pi) = -1$ and $\sin(\pi) = 0$.\n\n5. Substitute these values back: $$e^{i\pi} = -1 + i \cdot 0 = -1.$$\n\n6. Therefore, the value of $f(x) = e^{i\pi}$ is $-1$.