Math Problem Statement

f(x)=x²-5x ​g(x)=4x+1 (2f-g)(x)

Solution

To solve (2fg)(x)(2f - g)(x), we need to calculate the expression 2f(x)g(x)2f(x) - g(x) for the given functions f(x)f(x) and g(x)g(x).

Given Functions:

  • f(x)=x25xf(x) = x^2 - 5x
  • g(x)=4x+1g(x) = 4x + 1

Step 1: Find 2f(x)2f(x)

Multiply f(x)f(x) by 2: 2f(x)=2(x25x)=2x210x2f(x) = 2(x^2 - 5x) = 2x^2 - 10x

Step 2: Find g(x)g(x)

The function g(x)g(x) is already given: g(x)=4x+1g(x) = 4x + 1

Step 3: Compute 2f(x)g(x)2f(x) - g(x)

Now, subtract g(x)g(x) from 2f(x)2f(x): [ (2f - g)(x) = 2x^2 - 10x

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Function Operations

Formulas

f(x) = x² - 5x
g(x) = 4x + 1
(2f - g)(x) = 2f(x) - g(x)

Theorems

Basic Algebraic Manipulation

Suitable Grade Level

Grades 8-10