Precalculus 2014
65

 PAGE: 72 SET: Exercises PROBLEM: 65

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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