Math Problem Statement

Given g, of, x, equals, minus, 5, x, plus, 2g(x)=−5x+2, find g, of, minus, 4g(−4).

Solution

Given the function g(x)=5x+2g(x) = -5x + 2, we need to find g(4)g(-4).

To do this, substitute 4-4 for xx in the function:

g(4)=5(4)+2g(-4) = -5(-4) + 2

Now, calculate step by step:

  1. Calculate 5×4-5 \times -4:

5×4=20-5 \times -4 = 20

  1. Add 2 to the result:

20+2=2220 + 2 = 22

Therefore, g(4)=22g(-4) = 22.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:

  1. What is the general form of a linear function?
  2. How do you evaluate a function for a given input?
  3. How does the graph of g(x)=5x+2g(x) = -5x + 2 look like?
  4. What does the slope represent in a linear function?
  5. How do you find the x-intercept and y-intercept of a linear function?

Tip: When substituting a value into a function, carefully follow the order of operations: perform multiplication and division first, then addition and subtraction.

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Math Problem Analysis

Mathematical Concepts

Linear functions
Substitution

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9