Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 9a

Chapter 3, Problem 9a

Find the domain of each function. f(x) = 1/(x+7) + 3/(x-9)

Verified step by step guidance

Step 1: Recall that the domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions, the function is undefined when the denominator equals zero.

Step 2: Identify the denominators in the given function. The function is f(x) = 1/(x+7) + 3/(x-9). The denominators are (x+7) and (x-9).

Step 3: Set each denominator equal to zero to find the values of x that make the function undefined. Solve the equations x+7=0 and x-9=0.

Step 4: Solve x+7=0 to get x = -7, and solve x-9=0 to get x = 9. These are the values of x that make the denominators zero, so the function is undefined at x = -7 and x = 9.

Step 5: Write the domain of the function. The domain includes all real numbers except x = -7 and x = 9. In interval notation, the domain is expressed as (-∞, -7) ∪ (-7, 9) ∪ (9, ∞).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational functions, the domain is restricted by values that make the denominator zero, as division by zero is undefined. Understanding the domain is crucial for determining where the function can be evaluated.

Rational Functions

A rational function is a function that can be expressed as the ratio of two polynomials. In the given function f(x) = 1/(x+7) + 3/(x-9), each term is a rational expression. The behavior of rational functions is significantly influenced by their denominators, which can introduce restrictions on the domain.

Finding Restrictions in the Domain

To find the domain of a function, one must identify values that cause the denominator to equal zero. For the function f(x) = 1/(x+7) + 3/(x-9), we set the denominators (x+7) and (x-9) to zero and solve for x. The solutions, x = -7 and x = 9, indicate the points where the function is undefined, thus defining the domain.

Recommended video:

3:51

Domain Restrictions of Composed Functions

Related Practice

Textbook Question

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = = -x and g(x) = -x

633

views

Textbook Question

Evaluate each function at the given values of the independent variable and simplify. (a) f(-2), (b) f(1), (c) f(2)

114

views

Textbook Question

Use the graph of y = f(x) to graph each function g.

g(x) = -f(x) +3

779

views

Textbook Question

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = ∛(x − 4) and g(x) = x³ +4

609

views

Textbook Question

Use the graph of y = f(x) to graph each function g.

g(x) = f(-x)+3

1044

views

Textbook Question

Use the given conditions to write an equation for each line in point-slope form and general form. Passing through (−2, 2) and parallel to the line whose equation is 2x-3y-7=0

1181

views