# How do you find the domain and range of # y = sin^(-1)(x^2)#?

##### 1 Answer

Domain:

Range:

#### Explanation:

**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