/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 Find each value if \(f(x)=3 x-4\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 63

Find each value if \(f(x)=3 x-4\). $$ f(a) $$

Short Answer

Expert verified
\( f(a) = 3a - 4 \)

Step by step solution

01

Understand the Function Notation

The function given is \( f(x) = 3x - 4 \). This means for whatever value is substituted for \( x \) in \( f \), we compute it using the expression \( 3x - 4 \). Here, we need to find \( f(a) \), so we'll substitute \( a \) into the function.
02

Substitute the Value in the Expression

Replace \( x \) with \( a \) in the function \( f(x) = 3x - 4 \) to find \( f(a) \). This gives the expression \( f(a) = 3a - 4 \).
03

Simplify the Expression

The expression \( 3a - 4 \) is already in its simplest form because it combines all the operations possible with the given variable \( a \). Thus, \( f(a) = 3a - 4 \) is the simplified result and the value of the function at \( a \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Function Evaluation
Function evaluation is the process of finding the output of a function given a specific input. When you have a function, like \( f(x) = 3x - 4 \), it's essentially a rule that tells you how to transform an input \( x \) into an output. Evaluating a function involves substituting a number or expression for the variable in the function's formula.

The process is quite straightforward:
  • Identify the input value you need to substitute. In this case, we were asked to find \( f(a) \).
  • Replace the variable in the function's formula with the chosen input value. Therefore, \( f(a) = 3a - 4 \).
  • Compute the result using the arithmetic operations defined in the function. This will provide the output for the given input.
Understanding function evaluation is crucial as it lays the foundation for solving more complex problems in algebra and calculus.
Algebraic Expression
An algebraic expression is a mathematical phrase that includes numbers, variables, and operations like addition, subtraction, multiplication, and division. These expressions represent quantities and are used to express a mathematical relationship.

In our example, the function expression \( 3x - 4 \) is algebraic. It comprises:
  • The coefficient 3, which multiplies the variable \( x \). It denotes that \( x \) is scaled by 3.
  • The variable \( x \), which is a placeholder that can represent various values.
  • The constant -4, which is subtracted from the product of 3 and \( x \).
This simple expression follows the rules of algebra, and understanding it helps make sense of more complex mathematical problems by breaking them down into manageable parts.
Variable Substitution
Variable substitution involves replacing a variable in an expression or formula with a specific value or another expression. This concept is vital for evaluating functions, simplifying expressions, and solving equations.

In function notation, substituting the value involves:
  • Identifying the variable to substitute. In our example, it's \( x \).
  • Replacing this variable with the desired value, such as \( a \) in \( f(a) = 3a - 4 \).
  • Ensuring that the substitution is done consistently throughout the expression.
Through substitution, you can transform a general expression into a specific result, making calculations possible. Mastering this process is vital for tackling a wide variety of mathematical tasks.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

CHALLENGE If \(f(3 a-1)=12 a-7,\) find one possible expression for \(f(x)\)

Graph each function. Identify the domain and range. \(g(x)=|x|-4\)

OPEN ENDED Write a relation of four ordered pairs that is not a function. Explain why it is not a function.

Masao has a long-distance telephone plan where she pays 10\(\notin\) for each minute or part of a minute that she talks, regardless of the time of day. How much would a call that lasts 9 minutes and 40 seconds cost?

REVIEW What is the solution set of the inequality? $$6-|x+7| \leq-2$$ $$ \begin{array}{l}{\mathbf{F}-15 \leq x+\leq 1} \\ {\mathbf{G}-1 \leq x \leq 3} \\\ {\mathbf{H} x \leq-1 \text { or } x \geq 3} \\ {\mathbf{J} \quad x \leq-15 \text { or } x \geq 1}\end{array} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.