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

Algebra Level 3

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

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

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

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