Why does this lambda require *arg, what difference does it make?

Question

I came across a pretty clever little function that takes two functions, applies one on top of each other given an argument x:

def compose(f,g):
    return lambda *x: f(g(*x))

Now my issue is with *x, as I don't see it really doing anything here. Why couldn't it be simple x (without the asterisk)?

Here are my tests:

>>> def compose(f,g):
...   return lambda *x: f(g(*x))
... 
>>> this = lambda i: i+1
>>> that = lambda b: b+1
>>> compose(this,that)(2)
4

>>> def compose(f,g):
...   return lambda x: f(g(x))
... 
>>> compose(this,that)(2)
4

>>> def compose(f,g):
...   return lambda *x: f(g(*x))
... 
>>> compose(this,that)(2,2)
TypeError: <lambda>() takes exactly 1 argument (2 given)

Answer 1

If g (that in your tests) can also take a variable number of arguments, then lambda *x: f(g(*x)) can be useful.

Otherwise, not so much.

The aim is to allow the composed function to be invoked with any number of arguments, and for all these arguments to be passed to the inner function in the composition.