Math Problem Statement

Given g, of, x, equals, minus, 4, x, minus, 4g(x)=−4x−4, find g, of, minus, 2g(−2)

Solution

To find g(2)g(-2), we use the function definition provided:

g(x)=4x4g(x) = -4x - 4

Now, substitute x=2x = -2 into the equation:

g(2)=4(2)4g(-2) = -4(-2) - 4

Simplifying:

g(2)=84=4g(-2) = 8 - 4 = 4

So, g(2)=4g(-2) = 4.

Do you want further details or have any questions?

Related Questions:

  1. What is g(0)g(0) for the same function?
  2. How would the function graph of g(x)=4x4g(x) = -4x - 4 look?
  3. What is the slope of the line represented by g(x)=4x4g(x) = -4x - 4?
  4. How do you find the x-intercept of the function g(x)g(x)?
  5. What is the y-intercept of g(x)g(x)?

Tip: For linear functions like g(x)=4x4g(x) = -4x - 4, the coefficient of xx gives you the slope of the line.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Functions
Substitution

Formulas

g(x) = -4x - 4

Theorems

Linear Function Theorem

Suitable Grade Level

Grades 7-9