Problem with after-change-functions hook

[user240]

I am trying to create a hook so as to run a function when a certain buffer
changes. I put this in a mode definition function:

(add-hook 'after-change-functions 'function nil t)

but the resulting hook appears to be global, as the function take effect on
all buffers!? What do I do to restrict the hook to the buffer that the mode
function was run?

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