Given the following function:
Does the function have a domain? If so, what is it?
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Given the following function:
Does the function have a domain? If so, what is it?
To determine the domain of the function , we need to focus on avoiding division by zero, which occurs when the denominator is zero.
Let's identify the denominator of the function:
Next, we set the denominator equal to zero and solve for :
This calculation shows that the function is undefined when . Thus, the domain of the function is all real numbers except .
Therefore, the domain of the function is .
In terms of the provided choices, this corresponds to choice 4:
Yes,
Yes,
\( 22(\frac{2}{x}-1)=30 \)
What is the domain of the equation above?
The numerator can equal zero without any problems - this just means the function value is 0. Only when the denominator equals zero do we get division by zero, which is undefined.
It means x can be any real number except -4. So x can be -4.1, -3.9, 0, 100, but never exactly -4.
The domain is . The parentheses around -4 show it's excluded from the domain.
You get , which is undefined. This confirms why x = -4 must be excluded from the domain.
Yes! If the denominator factors into multiple terms, each factor set to zero gives a restriction. For example, excludes both x = 2 and x = -1.
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