# How do you find the domain and range of #cos^-1 [sqrt (1/4 - x^2)]#?

##### 1 Answer

#### Explanation:

The domain of the inverse cosine is

means

Of course the square root can't be negative so we're ok on that end and we up the bound to zero. Squaring,

That's two inequalities:

Other inequality,

That's always true, we can ignore it.

We're left with

Turning our attention to the radicand, given this range,

We know we'd hit the biggest cliche of trig sooner or later. A cosine of