# Is it a Power Function or a Function in a Power?

Algebra Level 4

$\large 2^x + 2^{f(x)} = 2$

Consider a real valued function satisfying the equation above. Find the range of the function $$f(x)$$.

Note: The domain of $$f(x)$$ is the largest subset of $$\mathbb{R}$$ allowed in which there exists a solution to the above equation.

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