Domains are values you're allowed to put in x, and still get 'y's - or, in functional notation, f(x) - that make sense. Domain restriction generally comes in a few flavors:
A) Division by 0
B) SQRT of a negative
C) Arcsin/arccos of a number that's not between -1 and 1 inclusive
D) log of 0 or a negative
E) Tangent of 90 degrees or 270 degrees
All of the above are FORBIDDEN! If you don't know C-E, don't worry about them. Basically, f(x)=1/x has a domain of x <> 0 since you can't but 0 in for x. That's the same as (-infinity, 0) U (0, infinity).
If it were f(x) = 1 / (x-2), it would be all x not equal to 2. Just figure out what makes the denom 0.
In your function, all you do to x is multiply it by itself, and add 86 to it. All real numbers can be squared, and all real numbers can be increased by 86, so the domain is all real numbers.
The range of your function is all the values of f(x) that can be attained. This is generally a little trickier. Just remember that anything squared must be non-negative. So you take something that's non-negative, and add 86 to it. Lowest value you can have for anything non-negative is 0. So y will always be at least 86. If y were less than 86, x^2 would have to be negative, which doesn't happen in real numbers. So, the range is [86, inf). There's no limit to how high y can go.
Of note, you can artificially restrict domains and ranges of functions. Additionally, there are restrictions that make logical sense if the equation represents a real-life situation. Let's say you throw a ball, and y is how far the ball has dropped at time x. In that case, the domain of the function is [0, infinity), since we don't deal with negative time too well. If y was profit made on a product when it was bought by x people, x would have to be a positive integer, since half-people and negative people don't exist.