What is the domain of the exercise?
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What is the domain of the exercise?
To find the domain of the expression , we need to identify values of that make the denominator of the fraction zero.
Step 1: Identify the denominator of the fraction, which is .
Step 2: Set the denominator equal to zero to find the values to exclude:
Therefore, is the value that makes the denominator zero, so it must be excluded from the domain.
Given the choices, the correct answer is .
Therefore, the domain of the expression is all real numbers except .
This implies that the correct choice is:
x≠3
Select the the domain of the following fraction:
\( \frac{6}{x} \)
The domain is all possible input values. Since division by zero is undefined, any x-value that makes the denominator zero must be excluded from the domain, regardless of what the numerator equals.
Domain asks: "What x-values are allowed?" Solving asks: "What x-values make the equation true?" These are completely different questions with different answers!
No! A numerator can equal zero - that just makes the whole fraction equal zero. Only when the denominator equals zero do we have an undefined expression.
You can write it as or "all real numbers except 3" or in interval notation: .
Find the values that make any denominator zero. If you have , then exclude both x = 2 and x = -1 from the domain.
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