Question
What are the domain and range of the real-valued function
The domain is
The domain is
The domain is
The domain is
The domain is
The domain is
The domain is
The domain is
Ask by Beck Osborne. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain is
Solution
-
The function is given by
-
Since the square root function is defined only for non-negative arguments, we require that
-
Solving the inequality:So, the domain is
. -
Next, we determine the range. The square root term
is always non-negative. Its minimum value is obtained when : -
Substitute this value in the function:As
increases beyond 3, increases, and thus increases. Therefore, takes on all values greater than or equal to . -
Thus, the range of the function is:
The correct answer is:
The domain is
The domain is
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Simplify this solution Extra Insights
To find the domain of the function
Now for the range, we note that the smallest value that
So the correct answer is: The domain is
Do you know that square roots have a fascinating history? They were first used by the ancient Babylonians around 2000 BCE! They developed methods for approximating square roots, long before modern algebra emerged. Such a clever bunch to tackle such complex concepts so early!
If you’re looking to dive deeper into the world of functions and their properties, consider exploring the works of mathematicians like Descartes or even learning about how functions are used in programming for coding algorithms! Understanding these concepts will sharpen your problem-solving skills and you’ll impress your friends with your mathematical prowess.
