Select the domain of the following fraction:
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Select the domain of the following fraction:
Let's examine the given expression:
As we know, the only restriction that applies to a division operation is division by 0, since no number can be divided into 0 parts, therefore, division by 0 is undefined.
Therefore, when we talk about a fraction, where the dividend (the number being divided) is in the numerator, and the divisor (the number we divide by) is in the denominator, the restriction applies only to the denominator, which must be different from 0,
However in the given expression:
the denominator is 16 and:
Therefore the fraction is well defined and thus the unknown, which is in the numerator, can take any value,
Meaning - the domain (definition range) of the given expression is:
all x
(This means that we can substitute any number for the unknown x and the expression will remain well defined),
Therefore the correct answer is answer B.
Determine if the simplification shown below is correct:
\( \frac{7}{7\cdot8}=8 \)
The domain restriction only applies to the denominator. Since x is in the numerator, it can equal zero without making the fraction undefined. is perfectly valid!
If we had , then we'd need x ≠ 0 because division by zero is undefined. The variable's position matters!
Think of it this way: you can't divide by zero, but you can divide zero by something. So only worry about what's below the fraction line (the denominator).
Yes! If the denominator was something like , it's never zero for real numbers, so the domain would still be all real numbers. But if it was , then no domain exists.
'All X' means the domain includes every possible real number. There are no restrictions on what values x can take in this expression.
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