Math Problem Statement

Given f, of, x, equals, 3, x, minus, 3f(x)=3x−3, find f, of, minus, 4f(−4)

Solution

We are given the function equation f(x)=3x3f(x) = 3x - 3. To find f(4)f(-4), we simply substitute x=4x = -4 into the function equation:

f(4)=3(4)3f(-4) = 3(-4) - 3

Let's calculate it step by step:

f(4)=123f(-4) = -12 - 3

f(4)=15f(-4) = -15

So, f(4)=15f(-4) = -15.

Would you like more details or have any other questions?


Here are 8 related questions to expand your understanding:

  1. What is f(0)f(0) for the function f(x)=3x3f(x) = 3x - 3?
  2. How would you find the value of f(2)f(2) for this function?
  3. What is the general formula to determine the slope of a linear function?
  4. How do you determine the y-intercept of a linear function?
  5. Can you rewrite the function f(x)=3x3f(x) = 3x - 3 in the form y=mx+by = mx + b and identify mm and bb?
  6. What is the inverse function of f(x)=3x3f(x) = 3x - 3?
  7. How do you graph the function f(x)=3x3f(x) = 3x - 3?
  8. What are the key properties of linear functions like f(x)=3x3f(x) = 3x - 3?

Tip: When solving a function, always substitute the given value carefully and follow the order of operations to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Function Evaluation
Substitution

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9