Linear Mappings With Differentiation

Question

For part (a): To find the Kernel of L, I set f '(x) - f^-1(x) = 0, and try to find all cases where f '(x)=f^-1(x). However, this leads me nowhere. Am I taking the wrong approach?

Answer 1

We have

$$I(f)=f$$ since $I$ is the identity map so you should solve the differential equation $$f'-f=0$$