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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 30E

**(a)**

To determine

**To find:** The function

Expert Solution

The sum of the functions

**Given:**

The functions are

**Result used:**

The sum of the functions

**Calculation:**

Substitute the value of

As the radicand cannot take negative values,

On simplification,

Also

Simplify the above inequality as follows.

So the value of *x* lies in the interval

Hence, the domain of

So the combined domain is

Therefore, the domain of

**(b)**

To determine

**To find:** The function

Expert Solution

The function

**Result used:**

The function

**Calculation:**

Substitute the value of

From part (a), the domain of the function

Therefore, the value of the given function is

**(c)**

To determine

**To find:** The function

Expert Solution

The product function

**Result used:**

The product function

**Calculation:**

Substitute the value of

From part (a), the domain of the function

Therefore, the value of the given function is

**(d)**

To determine

**To find:** The function

Expert Solution

The quotient function is

**Result used:**

The quotient function

**Calculation:**

Substitute the value of

Thus, the quotient function is defined when the denominator is not equal to 0.

Hence, the function is

Simplify the equation

So, the numbers −1 and 1 are excluded from the domain.

From part (a), the domain of the function

Remove −1 and 1 from

Therefore, the domain of the function is

Therefore, the value of the given function is