The function $f(x)$ satisfies
\[f(2^x) + xf(2^{-x}) = 1\]for all real numbers $x.$  Find $f(2).$
Question:
The function $f(x)$ satisfies
\[f(2^x) + xf(2^{-x}) = 1\]for all real numbers $x.$  Find $f(2).$
Answer:
Let's think step by step.

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The function $f(x)$ satisfies
\[f(2^x) + xf(2^{-x}) = 1\]for all real numbers $x.$  Find $f(2).$
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