Question

For which function is f(x) not equal to f -1(x)?

Answer 1

A function and its inverse are mirror images of each other across the line y=x. Since you want the function to be its own inverse, you want the function to have symmetry about the line y=x. All of these functions have that symmetry except ...

... c. f(x) = 2x

In the attached graph, the purple line shows no symmetry about y=x.