Need a little help getting started. Thanks!

If given F(R,R) the collection of all functions f:R->R.

1. Then how can I show F(R,R) is a vector space over R, the field of real numbers.

2. If L(f)=f(sqrt(2)), then how can I show that L:F(R,R)->R, is a linear transformation, what is the rank of L?