When you define a function $f$ in higher mathematics, you first write
$$f:A\rightarrow B$$
Here $A$ will denote the set the function is from (the domain) and $B$ will denote the section the function is going to (the codomain).
After this, you (generally) give a formula expressing how the function is defined. For example we could write "$f:\mathbb{N}\rightarrow\mathbb{N}$ defined by $f(n)=n+1$."
In the image you've attached, you've got a function called $f^{-1}$ which goes from whatever $N_b$ is (probably the natural numbers in base $b$) to $N_{10}$ (probably the natural numbers in base $10$). I would imagine that they have given you a definition for $f$ in a previous problem, or in the preceding chapter, or something.
It seems like there is a mistake in the problem - an extra $N$ before $N_b$ in the definition of $f$.
The problem should be very easy. If $f$ is one-to-one, then there is a unique element of $N_{10}$ associated with each element of $N_{b}$ in the image of $f$. (Which is probably all of $N_b$, as if not $f^{-1}$ is not well defined.)