Function

One-Many is not a function because

One input cannot produce multiple outputs

A many-to-one function does not have an inverse function

Only one-to-one has

Key idea

For an inverse to exist, the function must be one-to-one
➡ The parabola must pass the horizontal line test

A full parabola fails this test, so we restrict the domain to one side of the vertex.

“Is its own inverse” means:
when you find the inverse of the function and draw it, the inverse falls exactly on top of the original graph.
That is why the last graph does is it not its own inverse

If it has an inverse it is a one-one function

For a composite function to exist

All outputs of the function are allowed inputs of the function.

range of f is not a subset of the domain of f.

Format for range

Area under speed time graph is the the distance only

Not displacement.