In the function below the boldfaced $\mathbf{x}$ is the vector of "all the other $x$'s besides $x_i$, evaluated at $x_i^*$." Does the following notation convey that? If not, or if there is a better way to notate this, I appreciate the advice.
$f^* =f(x_i^* , \mathbf{x}) \:\:\:\:; \:\:\:\:\mathbf{x}=\mathbf{x}(x_i^*)$