Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

문제 53

3장, 문제 53

In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. f(g(1))

Name: College Algebra
Author: Blitzer
ISBN: 9780136970514

검증된 단계별 안내

Identify the composite function to evaluate: \(f(g(1))\). This means you first find \(g(1)\), then use that result as the input for \(f\).

Look up the value of \(g(1)\) in the \(g(x)\) table. According to the table, when \(x = 1\), \(g(1) = 1\).

Now, use the value \(g(1) = 1\) as the input for the function \(f\). So, you need to find \(f(1)\).

Look up the value of \(f(1)\) in the \(f(x)\) table. According to the table, when \(x = 1\), \(f(1) = 5\).

Therefore, the value of the composite function \(f(g(1))\) is \(f(1)\), which corresponds to the value found in the previous step.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Evaluation

Function evaluation involves finding the output value of a function for a given input. Using the tables, you locate the input value in the x-column and read the corresponding function value from the f(x) or g(x) column. This is essential for determining values like g(1) or f(g(1)).

Composite Functions

A composite function, denoted as f(g(x)), means applying one function to the result of another. First, evaluate the inner function g at x, then use that output as the input for f. Understanding this process is key to correctly evaluating expressions like f(g(1)).

Using Tables to Represent Functions

Tables provide discrete values of functions for specific inputs, allowing evaluation without explicit formulas. By matching input values to outputs in the tables, you can perform operations like composition. This method is useful when functions are defined only by data points.

관련 실천

교과서 질문

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

628

views

교과서 질문

Use the graph of y = f(x) to graph each function g. g(x)=2f(x-1)

924

views

교과서 질문

Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = x² - 2

1153

views

교과서 질문

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = x+4, g(x) = 2x + 1

850

views

교과서 질문

In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g (x) = √(x + 2) (x = = −2, −1, 2, 7)

128

views

교과서 질문

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

855

views