Given a function such that

(1)

- Evaluate .
- Prove that is one to one.
- Prove that for all .
- Find the range of .
- Sketch the graph of .

**Solution**

- Setting at we have that
However,

Thus .

- Let such that . Thus,
Hence is .

- Setting we have
since is strictly decreasing in .

- because .
- The graph is seen at the following figure: