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

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Answer 1 · 2016-11-25T15:04:33

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

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

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

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

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

$0 <= x^2 <=2$

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

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