Working problem from textbook. Given that f is continuously differentiable from R^n to R^m and determinant matrix at f(x') is rank m. What is to show is not important because I have difficulty in first step.

Suggestion says to use Implicit Function Theorem but Implicit Function Theorem refers to function F from R^n X R^m ---> R^m. It seems I must define a F from given premise and then use the theorem but I do not know how to define this F using the premise.