1. The problem is to understand the function $\varphi(|x|)$ where the input is the absolute value of $x$. 2. The absolute value function $|x|$ outputs $x$ if $x\geq0$ and $-x$ if $x<0$. 3. Applying $\varphi$ to $|x|$ means evaluating $\varphi$ at non-negative values only, since $|x|\geq0$ for all real $x$. 4. Without an explicit definition of $\varphi$, we can't simplify further, but typically $\varphi(|x|)$ is an even function if $\varphi$ is defined for non-negative inputs and extended to negative inputs via $|x|$. 5. If you provide a specific form or expression for $\varphi$, we can analyze or plot it further.