Math Problem Statement

Знайди область визначення функції y = √(3 - x + 5.2 - 81). Вибери правильну відповідь.

Solution

To find the domain D(f)D(f) of the function given:

y=3x+5.281y = \sqrt{3 - x + 5.2 - 81}

we need to analyze the expression inside the square root because the square root function is only defined for non-negative values. Therefore, we need:

3x+5.28103 - x + 5.2 - 81 \geq 0

Simplify the expression:

  1. 3+5.2=8.23 + 5.2 = 8.2
  2. 8.281=72.88.2 - 81 = -72.8

This gives:

x72.80-x - 72.8 \geq 0

or

x72.8x \leq -72.8

Thus, the domain of the function D(f)D(f) is:

(,72.8](-\infty, -72.8]

Now, looking at the answer choices, it appears none of the provided options match this exact result. Therefore, the correct response would be:

"Інша відповідь" (Another answer)

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Math Problem Analysis

Mathematical Concepts

Domain of a Function
Square Root Function
Inequalities

Formulas

√(expression) is defined when expression ≥ 0

Theorems

Properties of square roots in functions

Suitable Grade Level

Grades 9-10