Does the equation \( 2 x y=1 \) represent \( y \) as a function of \( x \) ?

To determine whether the equation \( 2xy = 1 \) represents \( y \) as a function of \( x \), we need to solve for \( y \) in terms of \( x \). Starting with the equation: \[ 2xy = 1 \] we can isolate \( y \) by dividing both sides by \( 2x \) (assuming \( x \neq 0 \)): \[ y = \frac{1}{2x} \] This expression shows that for each non-zero value of \( x \), there is a corresponding value of \( y \). Therefore, \( y \) can be expressed as a function of \( x \) when \( x \neq 0 \). However, it is important to note that the equation does not define \( y \) for \( x = 0 \) because division by zero is undefined. Thus, while \( y \) can be expressed as a function of \( x \) for all \( x \) except \( 0 \), it does not represent \( y \) as a function of \( x \) over the entire set of real numbers. In conclusion, the equation \( 2xy = 1 \) represents \( y \) as a function of \( x \) for \( x \neq 0 \).