(Hypatia 2024, Question 2, CEMC - UWaterloo)

For a positive $3$-digit integer $n$, $f(n)$ is equal to the sum of $n$ and the digits of $n$. For example, $f(351)=351+3+5+1=360$.

Note: The decimal representation of a $3$-digit number $abc$ is $a \cdot 10^2 + b \cdot 10 + c$. For example, $836 = 8 \cdot 10^2 + 3 \cdot 10 + 6$.
(a) What is the value of $f(132)$?
(b) If $f(n)=175$, what is the value of $n$?
(c) If $f(n)=204$, determine all possible values of $n$.

Answer Submission Note(s)
In part (c), sort your answers in ascending order and separate them with a comma.
Separate the answers for each part with a single space.
For example: "a b c1,c2"