Find the domain of the function $f(x) = \sin^{-1}\frac{x^2}{2}$
Answer & explanation
Correct answer: option 1
$f(x) = \sin^{-1}\frac{x^2}{2}$
We must have $0 ≤ \frac{x^2}{2}≤1$
$⇒0≤x^2≤2$
$⇒-\sqrt{2}≤x≤\sqrt{2}$
So, domain is $[-\sqrt{2}, \sqrt{2}]$
Find the domain of the function $f(x) = \sin^{-1}\frac{x^2}{2}$
Correct answer: option 1
$f(x) = \sin^{-1}\frac{x^2}{2}$
We must have $0 ≤ \frac{x^2}{2}≤1$
$⇒0≤x^2≤2$
$⇒-\sqrt{2}≤x≤\sqrt{2}$
So, domain is $[-\sqrt{2}, \sqrt{2}]$