I have two questions about the element-wise function of matrices. Let $X\in\mathbb{R}^{m\times n}$. Let $f$ be an element-wise invertible non-linear function.
Question 1: The pseudoinverse (Moore-Penrose inverse) $X^{\dagger}$ is known. Can $(f(X))^{\dagger}$ be expressed by $X^{\dagger}$?
Question 2: Let $W\in\mathbb{R}^{n\times q}$ and $\Delta\in\mathbb{R}^{n\times q}$. Can $f(X(W+\Delta))$ somehow be expressed by the product of $f(XW)$ and another matrix?