I am relatively new to differential geometry. I am studying it from Fecko Textbook on differential geometry. As soon as he introduces the concept of lie derivative,he asks to do exercise 4.2.2 in picture. The question is,how do I apply $\phi^*\psi$ to given function $\psi$. I know that $\phi^*$ transport fields against direction of flow. But how it does,I don't know.