1. The problem asks for the symmetric point of the function $$f(x) = \frac{x^{+1}}{x}$$.
2. First, simplify the function expression. Since $$x^{+1} = x$$, the function becomes $$f(x) = \frac{x}{x}$$.
3. For all $$x \neq 0$$, $$f(x) = 1$$ because $$\frac{x}{x} = 1$$.
4. The function is undefined at $$x=0$$ because division by zero is not defined.
5. The graph of $$f(x)$$ is a horizontal line $$y=1$$ for all $$x \neq 0$$.
6. To find the symmetric point, we consider points symmetric about the function or axis. Since the function is constant at $$y=1$$, the symmetric point on the curve must satisfy $$y=1$$.
7. Check the given options:
- a) (1, -1) has $$y=-1$$, not equal to 1.
- b) (1, 0) has $$y=0$$, not equal to 1.
- c) (0, 1) has $$y=1$$, but $$x=0$$ is not in the domain.
- d) (0, 0) has $$y=0$$, not equal to 1.
8. Since the function is undefined at $$x=0$$, the only valid points on the graph are where $$y=1$$ and $$x \neq 0$$.
9. None of the options exactly match a point on the function except (0,1) which is not in the domain.
10. Therefore, the symmetric point related to the function's behavior is best represented by option c) (0, 1) as it lies on the horizontal line $$y=1$$, the function's value everywhere else.
Final answer: c) (0, 1)
Symmetric Point
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