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The function is .
Horizontal line test:
A function has an inverse if and only if no horizontal line intersects its graph of the function in at most one point.
(1) The function is an one-to-one, because it passes the horizontal line test in the domain .Therefore the inverse of the function exist.
Domain of the function is .
Range of the function is .
(2) The function is an one-to-one, because it passes the horizontal line test in the domain . Therefore the inverse of the function exist.
Domain of the function is .
Range of the function is .
(1) To find the inverse of the function, consider and solve in terms of .
Since the domain of the function is , then
Now interchange and .
Replace .
The inverse of is .
The Domain of inverse funtion is the range of the function .
Domain of the function is .
(2) To find the inverse of the function, consider and solve in terms of .
Now interchange as and as .
The inverse of is
The Domain of inverse funtion is the range of the function .
Domain of the function is
Graph:
Graph the function for and ,
and .
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