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Math·Advanced Math·Nonlinear functions

hard

$$f(x)=9\left({\left(\frac{1}{8}\right)}^x+4\right)$$
The function $f$ is defined by the given equation. For all values of $x$, the value of $f(x)$ is greater than $k$, where $k$ is a constant. What is the greatest possible value of $k$?

A

0

B

4

C

36

D

288