Question

How do you find the domain and range of `y= x^2-2`?

Answer 1

Domain: `x in RRcolor(white)("XXX")`or, in interval notation, `color(white)("XXX")x in (-oo,+oo)`
Range: `y in [-2,+oo)`

Explanation:

I have assumed that the Universe of Discourse is the set of Real numbers (`RR`); the answer will be a bit different if you are working in Complex (`CC`) numbers.

`x^2-2` is defined for all Real values of `x`
`rArr` the Domain is all Real values.

Since (for Real values of `x`) `x^2 >=0`
`rArr y=x^2-2 >=-2`
and
since `x^2-2 rarr +oo` as `xrarr +-oo`
`rArr y`'s upper limit is `+oo`
`rArr` the Range is `[-2,+oo)`