# How do you find the implied range and domain of #arccos((x-1)^2)#?

##### 1 Answer

Range is

#### Explanation:

Over centuries, we have been told that the range of

or, for that matter,

In the

the range of

Here,

the conventional range of

and , as

The range of

Note that, piecewise,

Cosine value

y-graph:

graph{(y - arccos ((x-1)^2))((x-1)^2+(y-pi/2)^2-.04)=0}

Note the crest at

Y-graph:

graph{cos y - (x-1 )^2 =0 [0 60 -15 15]}

Graph for understanding Y-range:

graph{cos y-(x-1)^2=0[0 4 -10 10]}

This is the double graph for

The two separate graphs in the combined Y-graph:

graph{(cos y)^0.5 - (x-1 )=0 [0 60 -15 15]}

graph{(cos y)^0.5 +(x-1 ) =0 [0 60 -15 15]}

You can realize now the suppressed details in our restricted range