The word I is vocalic. It doesn't start with a consonant or end with a consonant, but put it after a word that ends in a consonant and that consonant bleeds over across the word boundary. Like this:
Am I? [aem'mai]
Do I? [du:wai] <glide [w] is the consonant form of /u/>
Like I? [laik'gai] <[g] is voiced /k]>
In Like I say, what you're hearing is an unreleased [k] followed by [g]. The [g] is inserted to balance out the syllable or word boundary.
In physiological terms, the vocal folds in anticipation of the oncoming vowel [ai] ("I"), begin to close in order to vibrate to produce a voiced sound. In closing, the folds do not release the puff of air that is characteristic of [k], making [k] sound unreleased and almost inaudible, and as the folds begin to vibrate, they voice /k/ to [g], its voiced counterpart, and hold it across the word boundary producing li[k]'[gai].
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