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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter T, Problem 3CDT

(a)

To determine

**To find:** The domain of the function

Expert Solution

The domain of the function

**Formula used:**

Domain: The set of all possible values of the independent variables in a function is called the domain of the function.

**Calculation:**

Consider the given function

The function is not defined if the denominator of the function equals to 0.

The denominator of the function

Thus,

Therefore, the function

Hence, from the definition stated above, it is clear that the domain of the function is

Thus, the domain of the function

(b)

To determine

**To find:** The domain of the function

Expert Solution

The domain of the function

**Formula used:**

Domain: The set of all possible values of the independent variables in a function is called the domain of the function.

**Calculation:**

Consider the given function

The function is not defined if the denominator of the function equals to 0.

The denominator of the function

The denominator is

It is clear that, the function

Hence, from the definition stated above, it is clear that the domain of the function is

Thus, the domain of the function

(c)

To determine

**To find:** The domain of the function

Expert Solution

The domain of the function

**Formula used:**

Domain: The set of all possible values of the independent variables in a function is called the domain of the function.

**Calculation:**

Consider the given function

The function contains terms that is inside a square root.

It is known that the function is defined if the expression under the square root is non-negative.

That is,

And,

Thus,

Hence, from the definition stated above, it is clear that the domain of the function is

Thus, the domain of the function