Math Problem Statement

f(x)=3x^2−x+2, find f, of, minus, 4f(−4)

Solution

To solve f(4)f(-4) for the function f(x)=3x2x+2f(x) = 3x^2 - x + 2, follow these steps:

  1. Substitute x=4x = -4 into the function: f(4)=3(4)2(4)+2f(-4) = 3(-4)^2 - (-4) + 2

  2. Simplify the expression: f(4)=3(16)+4+2=48+4+2f(-4) = 3(16) + 4 + 2 = 48 + 4 + 2 f(4)=54f(-4) = 54

Thus, f(4)=54f(-4) = 54.

Let me know if you'd like further details on the steps!

Here are 5 related questions:

  1. What is the derivative of f(x)=3x2x+2f(x) = 3x^2 - x + 2?
  2. How do you find the maximum or minimum value of f(x)f(x)?
  3. What happens if you solve f(x)=0f(x) = 0?
  4. What is f(1)f(1) for the given function?
  5. Can you express f(x)f(x) in factored form?

Tip: Always check if the function can be simplified before solving for specific values!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Quadratic Functions

Formulas

f(x) = ax^2 + bx + c
Substitution into a function

Theorems

Quadratic Function Evaluation

Suitable Grade Level

Grades 8-10