Whether the below function is an increasing function and find out if the inverse of the function exists. If the inverse exists, find out the inverse of the function.
To find if the inverse of the function exists:
For the interval ,
Let us assume that if
Then,
Thus, the inverse of the function exists.
For the interval ,
Let us assume that if
Then,
Thus, the inverse of the function exists.
Hence, we get that the inverse of the function exists.
Inverse of the function:
For the interval ,
Replacing with , we get
On switching and , we get
Solving for , we get
Replacing with , we get
For the interval ,
Replacing with , we get
On switching and , we get
Solving for , we get
Replacing with , we get
Thus, Inverse of function is
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