Domain: x ; Range: -∞ < y < ∞. Hence the correct option is b.
The function is represented as y= 1/x. To determine the domain and range of this function, we need to consider the values of x for which the function is defined and the corresponding values of y that the function can take.
The function is defined for all real numbers except when the denominator is zero since division by zero is undefined. In this case, the denominator is x, so the function is undefined when x=0. Therefore, the domain excludes x=0, and it is expressed as x ≥ 0, indicating that x can take any real number greater than or equal to zero.
For the range, we need to consider the possible values of y. As x approaches 0 from the right (x→0+ ), the function approaches positive infinity (y→+∞). Similarly, as x becomes very large in either the positive or negative direction (x→±∞), the function approaches zero (y→0). Therefore, the range is expressed as -∞ < y < ∞, indicating that y can take any real value except 0.
Hence, the correct answer is B. Domain: x ; Range: -∞ < y < ∞. Hence the correct option is b.