Math Problem Statement

Giá trị nhỏ nhất của A = -5 + √(2x - 8) là ...

Solution

To find the minimum value of A=5+2x8A = -5 + \sqrt{2x - 8}, let’s analyze the problem:

  1. Domain of the square root function: The expression inside the square root, 2x82x - 8, must be non-negative: 2x80    x4.2x - 8 \geq 0 \implies x \geq 4. So, the domain of AA is x4x \geq 4.

  2. Expression for AA: Since 2x8\sqrt{2x - 8} is an increasing function, the smallest value of AA occurs at the smallest value of xx within the domain.

  3. Minimum value of AA: At x=4x = 4: A=5+2(4)8=5+0=5.A = -5 + \sqrt{2(4) - 8} = -5 + \sqrt{0} = -5.

Thus, the minimum value of AA is 5-5.

Do you want me to explain further details or verify any steps? Here are 5 related questions to deepen understanding:

  1. How do you determine the domain of a square root function?
  2. What happens to the value of AA as xx increases beyond the minimum xx?
  3. Why does the square root function impact the minimum of AA?
  4. Can the value of AA ever decrease below 5-5? Why or why not?
  5. How do we solve similar problems involving square roots in more complex equations?

Tip: Always start by identifying the domain of a function when working with square roots or logarithms.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Root Functions

Formulas

Square root function: \( \sqrt{x} \) is defined for \( x \geq 0 \)

Theorems

Domain of square root function
Behavior of increasing functions

Suitable Grade Level

Grades 9-10