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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 19a
Chapter 3, Problem 19a

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2.
ƒ(x)=3x+4, g(x)=2x-5

Verified step by step guidance
1
To find (ƒ+g)(x), we need to add the two functions ƒ(x) and g(x) together. This means we write (ƒ+g)(x) = ƒ(x) + g(x).
Substitute the given functions into the expression: (ƒ+g)(x) = (3x + 4) + (2x - 5).
Combine like terms by adding the coefficients of x and the constant terms separately: (3x + 2x) + (4 - 5).
Simplify the expression to get the combined function: (ƒ+g)(x) = 5x - 1.
Determine the domain of each function. Since both ƒ(x) = 3x + 4 and g(x) = 2x - 5 are linear functions, their domains are all real numbers, so the domain of (ƒ+g)(x) is also all real numbers.

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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 value. For functions ƒ(x) and g(x), (ƒ+g)(x) = ƒ(x) + g(x). This operation combines the expressions algebraically to form a single function.
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Adding & Subtracting Functions Example 1

Domain of a Function

The domain of a function is the set of all input values (x-values) for which the function is defined. When combining functions, the domain of the resulting function is the intersection of the domains of the original functions, ensuring all inputs are valid for both.
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Domain Restrictions of Composed Functions

Linear Functions

Linear functions have the form f(x) = mx + b, where m and b are constants. They are defined for all real numbers, so their domain is typically all real numbers unless otherwise restricted. Understanding this helps in determining the domain of combined linear functions.
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Linear Inequalities
Related Practice
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Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

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For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-8

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For the pair of functions defined, find (ƒg)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-7

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For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-6

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In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (5, -4), radius 7

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Textbook Question

For each piecewise-defined function, find (a) ƒ(-5), (b) ƒ(-1), (c) ƒ(0), and (d) ƒ(3).

f(x)={2+xif x<−4−xif −4≤x≤23xif x>2f(x) =\(\begin{cases}\)2 + x & \(\text{if }\) x < -4 \\-x & \(\text{if }\) -4 \(\leq\) x \(\leq\) 2 \\3x & \(\text{if }\) x > 2\(\end{cases}\)

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