Proving Differentiability of f given g'(x) < 0 $\forall$ x

[mathwizarddud]

Suppose the real valued $$g$$ is defined on $$\mathbb{R}$$ and $$g'(x) < 0$$ for every real $$x$$. Prove there's no differentiable $$f: R \rightarrow R$$ such that $$f \circ f = g$$.

 

[CompuChip]

See also here/