Dimension of images of large level sets

Let $k$ be a natural number. We consider $k$-times continuously differentiable real-valued functions $f\colon E\to \mathbb{R} $, where $E$ is some interval on the line having positive length. For $0<\alpha <1$ let $I_\alpha (f)$ denote set of values $y\in $ whose preimage $f^{-1}(y)$ has Hausdorff dimension at least $\alpha$. how large can (f)$, as $f$ ranges over all from into $\mathbb{R} $. show that sharp upper bound $\dim I_\alpha $(1-\alpha )/k$.