Consider is an odd function.

From the definition :

The composite function is .

                                        ( Since )

Here we can not decide whether it is either even or odd function.

When is an odd function then can be either even function or odd function.

So it depends on the function .

Case 1:

Consider is an even function.

From the definition : .

The composite function is .

                                     ( Since )

                                        ( Since )

.

When is an odd function and is an even function then is an even function.

Case 2:

Now consider is an odd function.

From the definition : .

The composite function is .

                                    ( Since )

                                    ( Since )

.

When and are odd functions then is an odd function.

is an odd function then can be either even function or odd function.

is an even function then is an even function.

is an odd functions then is an odd function.