Abs Sin Function E56074

1. The problem is to understand and simplify the given function $$f(x) = 0 + \left(0.8 \left( \left|x+4.5855\right| + 2\left|x+2.1855\right| + \left|x-0.21455\right| - \left(2\left|x+3.3855\right| + 2\left|x+0.98545\right|\right) \right) \frac{1+\sin\left(20.944(x+2.1855)\right)}{2} \right) + \left(-0.575 \left( \left|x-0.21455\right| + \left|x+4.5855\right| - 2\left|x+2.1855\right| \right) \left(1 - \sin\left(20.944(x+2.1855)\right) \right) \right)\right)$$. 2. This function involves absolute values and sine functions combined linearly. 3. To analyze or simplify, we can consider the function piecewise by evaluating the absolute values depending on the sign of the expressions inside. 4. The sine term oscillates between -1 and 1, so the factors $$\frac{1+\sin(\cdot)}{2}$$ and $$1 - \sin(\cdot)$$ modulate the amplitude. 5. The function is a sum of two parts, each multiplied by these sine-based weights. 6. Without specific $x$ values or further instructions, the function is best left in this form or evaluated numerically. Final answer: The function $$f(x)$$ is defined as above and involves piecewise absolute values and sinusoidal modulation; further simplification requires case-by-case analysis or numerical evaluation.