Given that the graph of the function is symmetric with respect to the origin, and $f(2) = 1$, find the value of $f(-2)$.

AlgebraFunctionsOdd FunctionsSymmetry
2025/6/14

1. Problem Description

Given that the graph of the function is symmetric with respect to the origin, and f(2)=1f(2) = 1, find the value of f(2)f(-2).

2. Solution Steps

Since the graph of the function is symmetric with respect to the origin, the function is an odd function.
For an odd function, we have f(x)=f(x)f(-x) = -f(x).
Given f(2)=1f(2) = 1, we want to find f(2)f(-2).
Using the property of odd functions, f(2)=f(2)f(-2) = -f(2).
Since f(2)=1f(2) = 1, then f(2)=1f(-2) = -1.

3. Final Answer

The final answer is -
1.

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