Two numbers are reciprocals if their product is equal to 1. If y and x are reciprocals and y ​> 1, then x must​ be:

Question

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Part 1
A.
between 0 and 1.
B.
less then​ -1.
C.
equal to 0.
D.
between 0 and​ -1.
E.
greater than 1.

Answer 1

If \( y \) and \( x \) are reciprocals, then their product is equal to 1:

\[ y \cdot x = 1 \]

Given that \( y > 1 \), we can solve for \( x \):

\[ x = \frac{1}{y} \]

Since \( y \) is greater than 1, \( \frac{1}{y} \) will be less than 1. Therefore, \( x \) must be:

\[ x < 1 \]

Since reciprocals are positive when \( y > 1 \), \( x \) must also be positive, meaning \( x \) is between 0 and 1.

Thus, the correct answer is:

A. between 0 and 1.