# Free and bound variables in a lambda-calculus term

For this term: $\lambda x.(f (g x))$, what are the free and bound variables?

I'm confused as to how to expand this so it will be easier to see. If I expand this will it be $\lambda x. \lambda f. \lambda g$?

• What do you mean by expanding? The second lambda term in your question has nothing to do with the first. What is your definition of free variables, and your definition of bound variables? – Gilles 'SO- stop being evil' Apr 6 '13 at 23:51

The free variables in the term you give are $f$ and $g$, $x$ is bound by the $\lambda$-binder.
I am also confused what you mean by "expanding"? But I guess you want to abstract away those free variables. If that is true, then you will get $\lambda x . \lambda f . \lambda g . f\ (g\ x)$ (or with the parameters permuted in another way.)