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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 4
Chapter 3, Problem 4

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2
(ƒ/g)(2)(ƒ/g)(2)

Verified step by step guidance
1
Understand that the notation (ƒ/g)(2) means the function ƒ divided by the function g, evaluated at x = 2. In other words, (ƒ/g)(2) = \(\frac{ƒ(2)}{g(2)}\).
Evaluate ƒ(2) using the function definition ƒ(x) = x + 1. Substitute x = 2 to get ƒ(2) = 2 + 1.
Evaluate g(2) using the function definition g(x) = x^2. Substitute x = 2 to get g(2) = 2^2.
Write the expression for (ƒ/g)(2) as \(\frac{ƒ(2)}{g(2)}\) = \(\frac{2 + 1}{2^2}\).
Simplify the fraction by performing the arithmetic operations in the numerator and denominator separately, then write the final simplified fraction.

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Key Concepts

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

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific value means substituting that value into the function's formula and simplifying to find the output.
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Evaluating Composed Functions

Function Operations (Division of Functions)

The division of two functions (ƒ/g)(x) means creating a new function by dividing the output of ƒ(x) by the output of g(x), expressed as (ƒ/g)(x) = ƒ(x) / g(x). It requires evaluating both functions at the same input and then dividing the results.
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Multiplying & Dividing Functions

Substitution and Simplification

To evaluate (ƒ/g)(2), substitute 2 into both ƒ(x) and g(x), then divide the results. Simplifying the expression involves performing arithmetic operations carefully to find the final value without using paper and pencil.
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Related Practice
Textbook Question

Fill in the blank to correctly complete each sentence. The y-intercept of the graph of y = -2x + 6 is ________.

Textbook Question

Fill in the blank(s) to correctly complete each sentence. For the function ƒ(x) = -4x + 2, ƒ(-2)= ______.

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2

(ƒ∘g)(2)(ƒ∘g)(2)

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Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x3? What is its range?

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Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. A(-6, 3), B(-6,8)

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