Counting functions problem 4

Could someone please check my answers for the following problems, especially b?

Consider the possible functions f:[7]$\displaystyle \longrightarrow$[9]?

a) How many have f(3)=8? How many have f(3)$\displaystyle \neq$8?

There is one object being distributed to one recipient for f(3)=8, plus 6 objects being distributed to 9 recipients. So there are $\displaystyle 1+9^{6}$ possible functions that have f(3)=8. For the second part of the question, $\displaystyle f(3)\neq8$ has 8 different functions plus 6 objects being distributed to 9 recipients. So there are $\displaystyle 8+9^{6}$ possible functions that have $\displaystyle f(3)\neq8$.

b) How many have $\displaystyle f(1) \neq5 $ and are one-to-one?

In this case we have 8 possible functions for $\displaystyle f(1) \neq5$ plus $\displaystyle (9)_{6}= 8+(9)_{6}$.

c) How many have $\displaystyle f_{i}$ even for all i?

There are 4 even numbers in the Codomain, which gives $\displaystyle 4^{7}$ distributions of 7 objects to 4 recipients.

d) How many have $\displaystyle rng(f)=\{5,6\}$?

That would be 7 objects distributed to 2 recipients, so $\displaystyle 2^{7}$.

e) How many in which $\displaystyle f^{-1}$ is not a function?

This would be the same as the total number of distributions of 7 objects to 9 recipients minus the number which have a one-to-one relationship which would be $\displaystyle (9)_{7}$.So the answer is $\displaystyle 9^{7}-(9)_{7}$.