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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 3
Chapter 3, Problem 3

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
(ƒg)(2)

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1
Understand that the notation \((\f g)(2)\) means the composition of functions \(f\) and \(g\) evaluated at \(x=2\), which is \(f(g(2))\).
First, evaluate the inner function \(g(2)\) by substituting \(2\) into \(g(x) = x^2\), so calculate \(g(2) = 2^2\).
Next, take the result from \(g(2)\) and substitute it into the function \(f(x) = x + 1\), so compute \(f(g(2)) = f(2^2) = f(4)\).
Evaluate \(f(4)\) by substituting \(4\) into \(f(x) = x + 1\), which means calculating \(4 + 1\).
The final value of \((f g)(2)\) is the result of \(f(4)\), which completes the evaluation of the composition.

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Key Concepts

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

Function Composition

Function composition involves applying one function to the result of another, denoted as (f∘g)(x) = f(g(x)). It means you first evaluate g at x, then use that output as the input for f. Understanding this process is essential to correctly evaluate composite functions.
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Evaluating Functions

Evaluating a function means substituting a specific value for the variable and simplifying the expression. For example, if f(x) = x + 1, then f(3) = 3 + 1 = 4. This skill is necessary to find the value of functions at given points.
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Order of Operations in Composite Functions

When evaluating composite functions like (f∘g)(2), you must first compute g(2) before applying f to that result. This order ensures accurate evaluation and avoids mistakes, as the inner function's output becomes the input for the outer function.
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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

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

Fill in the blank to correctly complete each sentence. The x-intercept of the graph of 2x + 5y = 10 is ________.

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

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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