Question

How do you find the domain of `f(x) = - sqrt(2 / (x^2 - 16))`?

Answer 1

You have to check:

• the denominator must be different from zero
• the expression under the square root must be positive

So we must have `x^2 - 16 != 0 => x != +-4`

And (the numerator doesn't interfere):

`x^2 - 16>=0 => x>=4 or x<=-4`

So, intersecting, we have:
`D := {x in RR : x>4 or x<-4}`