Consider the next hashing definishion of $f(x)$
$$f(1) = 100$$ $$f(x) = \operatorname{SHA-256}(f(x-1))$$
Where $x$ is a positive integer and SHA-256 is the hash algorithm. You can think of SHA-256 as pseudorandom number generator, it will take an integer input and output with a random number between $0$ to $2^{256}$.
And $g(x)$ that just counting down $f(2)$
$$g(x)= f(2) - x$$
And now let's create $k(n)$ as the $min(x)$ value that satisfy $g(n) < f(x)$ where $n$ is a positive integer greater then $1$. Just to be clear let me try another way to define $k(n)$. For each value of $n$ find the minimum value of $x$ in $f(x)$ that will satisfy $g(n) < f(x)$. So $k(n)$ is equal to that value.
I hope that my above explanation makes sense. Now my question is: How does the graph of $k(n)$ looks like, is it linear or some thing else?