Math Problem Statement

The functions f and g are defined as follows: f(x) = 3x^3 + 5 and g(x) = 4x - 1. Find f(-4) and g(-7). Simplify your answers as much as possible.

Solution

The image contains two functions: f(x)=3x3+5andg(x)=4x1f(x) = 3x^3 + 5 \quad \text{and} \quad g(x) = 4x - 1 The problem asks to evaluate:

  • f(4)f(-4)
  • g(7)g(-7)

Let's start by calculating both values.

For f(4)f(-4):

f(4)=3(4)3+5=3(64)+5=192+5=187f(-4) = 3(-4)^3 + 5 = 3(-64) + 5 = -192 + 5 = -187

For g(7)g(-7):

g(7)=4(7)1=281=29g(-7) = 4(-7) - 1 = -28 - 1 = -29

Thus, the results are:

  • f(4)=187f(-4) = -187
  • g(7)=29g(-7) = -29

Would you like more details on these calculations?

Here are some related questions:

  1. How do you evaluate a cubic function?
  2. What are common transformations of cubic functions?
  3. What happens if you input positive values for f(x)f(x)?
  4. How does the slope of g(x)=4x1g(x) = 4x - 1 affect its graph?
  5. What is the difference between linear and cubic functions?

Tip: Always simplify the powers and products first when evaluating functions with exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Evaluation
Cubic Functions
Linear Functions

Formulas

f(x) = 3x^3 + 5
g(x) = 4x - 1

Theorems

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Suitable Grade Level

Grades 9-12