Math Problem Statement

If f(x) = 2x^2 + 5√(x - 2), complete the following statement: f(3) = _____

Solution

Given the function f(x)=2x2+5x2f(x) = 2x^2 + 5\sqrt{x - 2}, substituting x=3x = 3 yields:

f(3)=23f(3) = 23

Would you like further clarification or have any questions? Here are five related questions to consider:

  1. What would the value of f(4)f(4) be using the same function?
  2. How would the function change if f(x)=3x2+4x2f(x) = 3x^2 + 4\sqrt{x - 2}?
  3. How can you determine the domain of the given function?
  4. What happens to the function when x<2x < 2?
  5. How does the square root function affect the overall shape of the graph?

Tip: When working with functions involving square roots, always ensure the expression inside the square root is non-negative to determine the domain correctly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Roots
Substitution

Formulas

f(x) = 2x^2 + 5√(x - 2)

Theorems

Square root properties
Substitution method

Suitable Grade Level

Grades 9-11