Problem $2$: Function inversion

Recall that a differential analyzer $($for our purposes$)$ consists only of parts that compute summation, multiplication, and integration. Diagrams as shows in class can be used to draw the connections between the components.

You have configured a differential analyzer computer to generate some function $f(t).$ In particular, you can assume that $f(t)$ is the output shaft of some integrator $($where $t$ is the variable of integration$).$ With as little modification as possible, describe how to re$-$wire the differential analyzer to generate the inverse function $f^{-1}(t).($That$\text{'}$s function inverse, not power of $-1.)$ Draw the diagram.

You can assume that the inverse exists and all the preconditions of the Inverse Function Theorem $($hint$!)$ are satisfied for $f.$

Hint: Note that the variable of integration for an integrator in a differential analyzer doesn't have to be $t$ but could be a variable output by another component.