Math Problem Statement

O domínio da função y = √(4x - 8) corresponde aos valores de x tal que:

Solution

To determine the domain of the function y=4x8y = \sqrt{4x - 8}, we must consider the condition under which the expression inside the square root is non-negative. The square root function is defined only for non-negative values.

Steps:

  1. The condition for the square root to be defined is: 4x804x - 8 \geq 0

  2. Solve the inequality: 4x8x24x \geq 8 \quad \Rightarrow \quad x \geq 2

Thus, the domain of the function is x2x \geq 2.

Correct Answer:

The correct choice is x2x \geq 2.


Would you like a deeper explanation or a graph of the function to illustrate this? Here are 5 related questions for further exploration:

  1. What is the range of y=4x8y = \sqrt{4x - 8}?
  2. How do square root functions behave when their domain changes?
  3. What happens if we change the function to y=4x+8y = \sqrt{-4x + 8}?
  4. Can a square root function ever have negative outputs?
  5. How would you express the domain and range of this function in interval notation?

Tip: Always check for restrictions like square roots and division by zero when determining a function's domain!

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Math Problem Analysis

Mathematical Concepts

Domain of a function
Inequalities
Square root functions

Formulas

√(expression) is defined if expression ≥ 0

Theorems

Properties of inequalities
Definition of the domain of square root functions

Suitable Grade Level

Grades 9-12