The function is .
Find the inverse function.
\Change to
.
.
Interchange and
.
Add to each side.
Divide each side by .
Apply inverse trigonometric property: .
The inverse function is .
Find the range of :
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Range of the tangent function: .
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The range of is
or
.
The domain of is range of
.
The range of is
.
Hence the domain of is
.
The range of of is domain of
.
The domain of is
.
Hence the range of is
.
The inverse function is .
The range of is
.
The domain of of is
.
The range of is
.