Question

What is the domain and range of `f(x) = sqrt(x^2-36)`?

Answer 1

Domain: `RR, (-oo,-6] uu [+6,+oo]`
Range: `RR, [0,+oo)`

Explanation:

`f(x)` is defined in the Real numbers provided
`color(white)("XXX")x^2-36 >= 0`
This will be true provided
`color(white)("XXX")x >= 6color(white)("XX")`or`color(white)("XX")x <=-6`
Therefore the domain (in `RR`) is `x in (+oo,-6]uu[+6,+oo)`

Since `sqrt("any real number")` is defined as the principle square root (i.e. `>= 0)`
the range is `f(x) in [0,+oo)`