Look at the following function:
What is the domain of the function?
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Look at the following function:
What is the domain of the function?
To solve this problem, we must determine the domain of the function .
To begin, the expression inside the square root, , must be greater than 0 for the square root to be real and the function to be defined. Thus, we set up the inequality:
Next, solve this inequality for :
Now, determine the intervals where is positive. Consider the intervals defined by the critical points and :
Test a value from each interval in the inequality :
Thus, the function is defined for in the intervals and .
This means that the domain of the function is:
Therefore, the solution to the problem is .
Given the following function:
\( \frac{5-x}{2-x} \)
Does the function have a domain? If so, what is it?
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