/*! 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 60 Let \(f(x)=3 x^{2}-x, g(x)=4 x-2... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 60

Let \(f(x)=3 x^{2}-x, g(x)=4 x-2,\) and \(k(x)=|x+3|\) Find the following. $$ g(-x) $$

Short Answer

Expert verified
g(-x) = -4x - 2

Step by step solution

01

Identify the given function

Given is the function \(g(x) = 4x - 2\).
02

Substitute \(-x\) for \ x

To find \(g(-x)\), substitute \(-x\) into the function \(g(x)\). This gives us: \(g(-x) = 4(-x) - 2\).
03

Simplify the expression

Simplify the expression \(g(-x) = 4(-x) - 2\). This results in: \(g(-x) = -4x - 2\).

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.

Substitution in Functions
Substitution in functions is a fundamental concept in algebra and calculus. It involves replacing the variable in a function with a different value or expression.
In the given exercise, we start with the function:
\(g(x) = 4x - 2\).
To find \(g(-x)\), we substitute \(-x\) for \(x\), like this: \(g(-x)\). This means wherever we see \(x\) in the function \(g(x)\), we replace it with \(-x\). When we do this, the equation becomes: \(g(-x) = 4(-x) - 2\).
This might look a bit confusing at first, but remember, substitution is just about making replacements. Think of it like following a recipe. If you need to use an ingredient but have a substitute, you simply swap it out.
Simplifying Expressions
Simplifying expressions is an essential skill in math as it makes problems more manageable and solutions clearer.
After substituting \(-x\) in place of \(x\), we have \(g(-x) = 4(-x) - 2\). The next step is to simplify this expression.

  • First, distribute the \(4\) across the \(-x\). This gives us \(4 \times (-x) = -4x\).
  • Then, include the \(-2\) from the original function.
So, we now get: \(g(-x) = -4x - 2\).
Simplifying expressions often involves combining like terms, removing parentheses by distributing, and reducing fractions. In this case, distributing the coefficient (4) over the substituted variable was our main focus.
Function Evaluation
Function evaluation means finding the value of a function for a given input. In this exercise, evaluating the function involved finding the value of \(g(x)\) when \(x = -x\).
Here鈥檚 a step-by-step look:
  • Start with the original function: \(g(x) = 4x - 2\)
  • Substitute the given input, which is \(-x\). This step transforms the original function into a new function: \(g(-x) = 4(-x) - 2\)
  • Finally, simplify this new function by performing arithmetic operations: we have \[g(-x) = -4x - 2 \]
Function evaluation helps to understand how a function behaves with different inputs and is a foundational concept in both basic and advanced mathematics.
When evaluating functions, always pay attention to the variable substitution and follow through with any required simplifications to ensure you get the correct result.

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

Let \(f(x)=3 x^{2}-x, g(x)=4 x-2,\) and \(k(x)=|x+3|\) Find the following. $$ k(-4) $$

Solve each problem. A right triangle has a hypotenuse of \(10 \mathrm{ft}\). If one leg is \(4 \mathrm{ft}\), then what is the length of the other leg?

Graph each function by plotting points and state the domain and range. If you have a graphing calculator, use it to check your results. $$ y=2 x-1 $$

Let \(f(x)=3 x^{2}-x, g(x)=4 x-2,\) and \(k(x)=|x+3|\) Find the following. $$ f(-1)+g(-1) $$

Solve each problem. Withholding A student sells ice cream bars. Her weekly salary is given by \(S(x)=0.40 x+200,\) where \(x\) is the number of ice cream bars sold. Her employer determines the amount withheld for taxes using the function \(W(x)=0.20 x\), where \(x\) is her weekly salary. Write the amount withheld as a function of the number of ice cream bars sold. Use composition.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.