Math Problem Statement
Solution
The problem asks for the domain of definition of the function , where for all .
The options provided are:
- (A)
- (B)
- (C)
- (D)
Solution:
To determine the domain of , we analyze the behavior of :
- is always non-negative for all real , i.e., .
- The value of depends on the relative magnitudes of , , and . There are no denominators, square roots of negative values, or undefined operations, so the function appears to be defined for all real numbers.
Checking for Critical Points:
Critical points occur when two or more elements of the set are equal:
- : Solve → , so or .
- : Already included.
- : Not directly problematic because is well-defined.
However, all elements in satisfy the function. The most plausible correction ##Upon reviewing the problem in detail, we conclude that the domain of depends on ensuring the maximum function has no undefined values.
The correct domain of is:
- (A) ( R^{-explan filtered!** !! skiped ##
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Math Problem Analysis
Mathematical Concepts
Functions
Set Theory
Analysis of Maximum Function
Formulas
f(x) = maximum {x, 1, x^2}
Theorems
Properties of maximum function
Suitable Grade Level
Grades 11-12
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