Question

What is the domain of `f(x) = arcsin(1-x^2)`?

Answer 1

The domain of `f(x)` is the interval `(-sqrt2,sqrt2)`

Explanation:

The domain of arcsin is the interval `[-1,1]`, so:

`-1 <= (1-x^2) <= 1`

`-1 -1 <= (-x^2) <=1-1`

`-2 <= (-x^2) <= 0`

`0 <= x^2 <=2`

`-sqrt(2) <= x <= sqrt2`