if the result of a function that produces the product of 16/25 and the reciprocal of the product of 4 and the sqare of the input and the sum of 1 and difference of 12/5 of the input is 1, find the square root of the function.

sure is hard to interpret your prose. If x is the input, then it appears that you are saying

(16/25) * 1/(4x^2)*(1+12x/5) = 1

somewhere there should be a subtraction, since you use the word "difference" but I can't figure out what, unless maybe there's a (12/5 - x) somewhere in there.

Now, I know that makes no sense, so why don't you write it out so we can work with it?