  For the Frechet space E=C^{\infty}(S^1) and for a smooth \phi: R to R, we
prove that the associated map E to E given by x mapsto\phi\circ x satisfies the
continuous B\Gamma--differentiability condition in Yamamuro's inverse function
theorem only if \phi is affine. Via more complicated examples, we also
generally discuss the importance of testing the applicability of proposed
inverse and implicit function theorems by this kind of simple maps.
