Skip to main content
Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 106
Chapter 3, Problem 106

Let ƒ(x)=3x2−4ƒ(x) = 3x^2 - 4 and g(x)=x2−3x−4g(x) = x^2 - 3x -4. Find each of the following.
(f+g)(2k)(f+g)(2k)

Verified step by step guidance
1
First, understand that (f+g)(x) means you add the functions f(x) and g(x) together, so (f+g)(x) = f(x) + g(x).
Write down the expressions for f(x) and g(x): f(x) = 3x^2 - 4 and g(x) = x^2 - 3x - 4.
Add the two functions together: (f+g)(x) = (3x^2 - 4) + (x^2 - 3x - 4).
Combine like terms in the expression: combine the x^2 terms, the x terms, and the constant terms.
After simplifying, substitute x with 2k in the resulting expression to find (f+g)(2k).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Function Addition

Function addition involves creating a new function by adding the outputs of two given functions for the same input. For functions f and g, (f+g)(x) = f(x) + g(x). This operation combines the values of f and g at each point x.
Recommended video:
4:46
Adding & Subtracting Functions Example 1

Function Evaluation

Function evaluation means substituting a specific input value into the function's formula to find the output. For example, to evaluate f(2k), replace every x in f(x) with 2k and simplify the expression.
Recommended video:
4:26
Evaluating Composed Functions

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents with coefficients. Understanding how to manipulate and simplify polynomials, such as squaring binomials and combining like terms, is essential for evaluating and adding functions like f(x) and g(x).
Recommended video:
06:04
Introduction to Polynomial Functions
Related Practice
Textbook Question

The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.

(c) y = ƒ(x+3) - 2

Textbook Question

Let ƒ(x)=3x2−4ƒ(x) = 3x^2 - 4 and g(x)=x2−3x−4g(x) = x^2 - 3x -4. Find each of the following.

(f/g)(−1)(f/g)(-1)

Textbook Question

The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.

(b) y = ƒ(x-2)

1
views
Textbook Question

The graph of a function ƒ is shown in the figure. Sketch the graph of each function defined as follows.

(d) y = |ƒ(x)|

Textbook Question

Work each problem. Find a function g(x)=ax+b whose graph can be obtained by translating the graph of ƒ(x)=2x+5 up 2 units and to the left 3 units.

5
views
Textbook Question

Let ƒ(x)=√(x−2)ƒ(x) = √(x-2) and g(x)=x2g(x) = x^2. Find each of the following, if possible.

(g○ƒ)(x)(g ○ ƒ)(x)