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

Verified step by step guidance

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.

Key Concepts

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

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.

Recommended video:

5:31

Graphing Rational Functions Using Transformations

Related Practice

Textbook Question

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

views

Textbook Question

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

Textbook Question

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

Textbook Question

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

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

Textbook Question

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

views

Textbook Question

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = ∛x + 1