1. **State the problem:** We need to find the value of the function $g(x) = \frac{1}{2} e^x (\sin x - \cos x)$ at $x=0$. 2. **Recall the formula:** The function is given by $$g(x) = \frac{1}{2} e^x (\sin x - \cos x)$$ 3. **Evaluate each part at $x=0$:** - $e^0 = 1$ - $\sin 0 = 0$ - $\cos 0 = 1$ 4. **Substitute these values into the function:** $$g(0) = \frac{1}{2} \times 1 \times (0 - 1)$$ 5. **Simplify the expression:** $$g(0) = \frac{1}{2} \times (-1) = -\frac{1}{2}$$ 6. **Final answer:** $$g(0) = -\frac{1}{2}$$ This means the function value at $x=0$ is $-\frac{1}{2}$.