How do you find the domain and range of # y = sin^(-1)(x^2)#?
Domain of the function
We know the inverse sin function is only defined for
The first one,
And we can solve the second one by taking the square root on both sides:
Now we combine this with our original interval, which we do by taking the most restrictive of the bounds:
And this is when our function is defined, so it must be the domain.
Range of the function
The inverse sine function usually ranges from