Domain of the function:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, we need to determine the values of x that make the function f(x) = x / (x - 2) defined.

Since division by zero is undefined, we need to exclude any values of x that would make the denominator (x - 2) equal to zero. Therefore, the function is not defined when x - 2 = 0. Solving for x, we find that x = 2.

Hence, the function is defined for all x-values except x = 2. Therefore, the domain of the function f(x) = x / (x - 2) is all real numbers except x = 2.

Range of the function:

The range of a function is the set of all possible output values (y-values) that the function can produce. To determine the range of the function f(x) = x / (x - 2), we need to analyze the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity:
When x becomes very large (positive infinity), the function approaches the value of 1. This is because the term x / (x - 2) can be simplified to 1 + (2 / (x - 2)). As x becomes larger and larger, the term 2 / (x - 2) approaches zero, resulting in f(x) approaching 1.

As x approaches negative infinity:
When x becomes very large (negative infinity), the function approaches the value of 1. This can be observed by simplifying the term x / (x - 2) as x approaches negative infinity. Again, the term 2 / (x - 2) approaches zero, resulting in f(x) approaching 1.

Therefore, the range of the function f(x) = x / (x - 2) is:
Range: {y | y ≠ 1}

In other words, the range of the function is all real numbers except for the value 1. The function can produce any output value except 1.

D of f(x) = R-{2} R of f(x) =R-{1}