Math Problem Statement

  1. Given g(x) = 6x + 4 and f(x) = 2x - 7 what is g(x) - f(x)?

A. 4x - 3 B. 8x - 3

D. 4x + 11

Solution

To find g(x)f(x)g(x) - f(x), you subtract the function f(x)f(x) from g(x)g(x).

Given: g(x)=6x+4g(x) = 6x + 4 f(x)=2x7f(x) = 2x - 7

Now, subtract f(x)f(x) from g(x)g(x):

g(x)f(x)=(6x+4)(2x7)g(x) - f(x) = (6x + 4) - (2x - 7)

Distribute the negative sign across f(x)f(x):

g(x)f(x)=6x+42x+7g(x) - f(x) = 6x + 4 - 2x + 7

Now, combine like terms:

g(x)f(x)=(6x2x)+(4+7)g(x) - f(x) = (6x - 2x) + (4 + 7)

g(x)f(x)=4x+11g(x) - f(x) = 4x + 11

So, the correct answer is:

D. 4x+114x + 11

Would you like more details or have any questions?


Here are 5 related questions:

  1. If h(x)=g(x)×f(x)h(x) = g(x) \times f(x), what is the expression for h(x)h(x)?
  2. What is the value of g(x)f(x)g(x) - f(x) when x=2x = 2?
  3. How would you find g(x)+f(x)g(x) + f(x)?
  4. What

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Subtraction of Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9