Question

What is the domain and range of `y = 1/(x^2 - 2)`?

Answer 1

Domain: `(-oo,-sqrt2) uu (-sqrt2,sqrt2) uu(sqrt2, +oo)`
Range: `(-oo,-1/2] uu (0, +oo)`

Explanation:

The domain can be determined by equating `x^2-2=0`

solving for x:
`x=+-sqrt2` and y is not defined when `x=+-sqrt2`

therefore the domain excludes `x=+-sqrt2`

For the Range:

`y` can have a value from -1/2 and lower and values higher than zero.

So that Range: `(-oo,-1/2] uu (0, +oo)`

graph{y=1/(x^2-2)[-20,20,-10,10]}

have a nice day!