Yikes. You've certainly got that backwards.
First of all, if what you mean by "the functions" is the internet-famous Harold Grant function stack, where INFP=Fi-Ne-Si-Te, that function model is inconsistent with Jung, inconsistent with Myers, has never been endorsed by the official MBTI folks, and has no respectable body of evidence behind it — and indeed, should really be considered all but
disproven at this point.
More generally, the MBTI can actually lay claim to quite a lot of scientific respectability in the reliability and validity departments, but that really only applies to the
dichotomy-centric MBTI — and not the "cognitive functions."
Carl Jung — mystical streak notwithstanding — was a believer in the scientific approach, and Myers took
Psychological Types and devoted a substantial chunk of her life to putting its typological concepts to the test in a way that Jung never had, and in accordance with the psychometric standards applicable to the
science of personality. Myers adjusted Jung's categories and concepts so that they better fit the data she gathered from thousands of subjects, and by the start of the 1960s (as the leading Big Five psychologists have acknowledged), she had a typology that was respectably tapping into four of the Big Five personality dimensions — long before there really was a Big Five. And twin studies have since shown that
identical twins raised in separate households are substantially more likely to match on those dimensions than genetically unrelated pairs, which is further (strong) confirmation that the MBTI dichotomies correspond to
real, relatively hard-wired underlying dimensions of personality. They're a long way from being simply theoretical — or pseudoscientific — categories with no respectable evidence behind them.
And on the other hand, the so-called "cognitive functions" have barely been studied. And the reason they've barely been studied is that, unlike the dichotomies, they've never been taken seriously by any significant number of academic psychologists.
If you're interested in reading more about the Harold Grant function stack (and its associated "tandems"), and about the relationship between the dichotomies and the functions, the place of the functions (or lack thereof) in the MBTI's history, and the tremendous gap between the dichotomies and the functions in terms of scientific respectability, you'll find a lot of potentially eye-opening discussion in
this TC Wiki page and the posts it links to.