Pregunta
For what values of x is the following expression a real number?
Ask by Harrington Vega. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The expression is real for all real numbers
Solución
To determine for which values of
is a real number, we need to ensure that the denominator is both real and non-zero.
Step-by-Step Analysis:
-
Denominator Must Be Real:
- The expression inside the square root,
, must be non-negative because the square root of a negative number is not a real number.
- The expression inside the square root,
-
Solve the Inequality:
-
Conclusion:
- For all real numbers
that are less than 8, the expression under the square root is positive, ensuring the denominator is real and non-zero.
- For all real numbers
Final Answer:
All real numbers x with x below eight. In other words, the expression is real for all x < 8
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Simplifique esta solución Beyond the Answer
For the expression to be a real number, the denominator must be positive, which means
In practical terms, you can’t have a negative number under the square root, as that would lead to complex numbers, which are not real. Always remember to check the conditions where the function is undefined—like division by zero—which can make a function blow up or become undefined at certain points!
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