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# Arcosine function

Given a function such that

(1)

1. Evaluate .
2. Prove that is one to one.
3. Prove that for all .
4. Find the range of .
5. Sketch the graph of .

Solution

1. Setting at we have that

However,

Thus .

2. Let such that . Thus,

Hence is .

3. Setting we have

since is strictly decreasing in .

4. because .
5. The graph is seen at the following figure: