To find the image of the function f(x) = x + sin(x) about the line y = -x, the reflection can be expressed as x = y + sin(y), which does not yield an explicit solution for y. The discussion explores whether images can be taken about functions, noting that reflections are typically defined with respect to points or lines. The functions f(x) and its reflection exhibit symmetry around the line y = x and intersect at the point (2π, 2π). The area under the reflected function g between specified limits is calculated to be 2π², leading to a final answer of 2. The exploration highlights the complexities of function reflections and their geometric interpretations.
