In Problems 63-74, the function is one-to-one. (a) Find its inverse function and check your answer. (b) Find the domain and the range of and .
To find:
a. Find its inverse function and check your answer.
Answer to Problem 61AYU
Solution:
a.
Explanation of Solution
Given:
Calculation:
a. Let .
Taking on both sides,
We get, ,
i.e.,
Change to and to .
Rewriting this, we get,
Also,
Here we verified that .
To find:
b. Find the domain and the range of and .
Answer to Problem 61AYU
Solution:
b. The domain of Range of .
The range of Domain of .
Explanation of Solution
Given:
Calculation:
b. When working with rational functions, domain elements must not create division by zero. Any not in the domain of must be excluded. So, we know that the domain of cannot contain 0.
For this, shows us that would not be an acceptable domain element, since it creates a zero denominator, setting , . Also exclude from the domain of . The domain of is .
For this, shows us that would not be an acceptable domain element, since it creates a zero denominator, setting , . Also exclude 0 from the domain of . The domain of is .
Therefore, The domain of Range of .
The range of Domain of .
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