Responde las siguientes preguntas.
1. Representa una ecuación inadmisible.
[tex]f(x)=\sqrt{x} x=5(3)-4(3)[/tex]
[tex]f(x)=\sqrt{x-1} x=0[/tex]
[tex]f(x)=\sqrt{x} x=4(3)-2(4)[/tex]
[tex]f(x)=\sqrt{x} x=6-3(1)[/tex]
Answer (2)
Evaluate x for each equation.
Check if the value of x is valid for the function f ( x ) .
Identify the equation where the value of x makes the square root negative.
The inadmissible equation is f ( x ) = x − 1 , x = 0 because it results in − 1 .
f ( x ) = x − 1 , x = 0
Explanation
Understanding Inadmissible Equations Let's analyze each equation to determine if it is inadmissible. An inadmissible equation is one where the value of x leads to an undefined result, such as a negative value under a square root.
Analyzing the First Equation
f ( x ) = x , x = 5 ( 3 ) − 4 ( 3 )
First, we calculate the value of x : x = 5 ( 3 ) − 4 ( 3 ) = 15 − 12 = 3 . Now, we check if this value of x is valid for the function f ( x ) = x . f ( 3 ) = 3 . Since the square root of 3 is a real number, this equation is admissible.
Analyzing the Second Equation
f ( x ) = x − 1 , x = 0
Here, x = 0 . We need to check if this value is valid for the function f ( x ) = x − 1 . f ( 0 ) = 0 − 1 = − 1 . Since the square root of -1 is not a real number (it's an imaginary number, i ), this equation is inadmissible.
Analyzing the Third Equation
f ( x ) = x , x = 4 ( 3 ) − 2 ( 4 )
First, we calculate the value of x : x = 4 ( 3 ) − 2 ( 4 ) = 12 − 8 = 4 . Now, we check if this value of x is valid for the function f ( x ) = x . f ( 4 ) = 4 = 2 . Since the square root of 4 is a real number, this equation is admissible.
Analyzing the Fourth Equation
f ( x ) = x , x = 6 − 3 ( 1 )
First, we calculate the value of x : x = 6 − 3 ( 1 ) = 6 − 3 = 3 . Now, we check if this value of x is valid for the function f ( x ) = x . f ( 3 ) = 3 . Since the square root of 3 is a real number, this equation is admissible.
Conclusion The second equation, f ( x ) = x − 1 , x = 0 , is inadmissible because it results in taking the square root of a negative number, which is not a real number.
Examples
Inadmissible equations, like the one identified, are crucial in various real-world applications, especially in physics and engineering. For instance, when modeling the motion of a pendulum, certain initial conditions might lead to equations with square roots of negative numbers, indicating that those conditions are physically impossible or that the model needs refinement. Similarly, in electrical circuit analysis, inadmissible solutions can highlight unrealistic parameter choices or circuit configurations. Recognizing and understanding inadmissible equations helps engineers and scientists ensure that their models accurately represent real-world phenomena and avoid nonsensical results.
The inadmissible equation from the given choices is f ( x ) = x − 1 , x = 0 because it results in − 1 , which is not a real number. The other equations yield valid real values for x when evaluated. Therefore, only the second equation is inadmissible due to a negative value under the square root.
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