Domain and Range of the Function f(x) = (x-2)/(3-x)

Domain:
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In other words, it represents the values of x for which the function can produce a valid output.

To determine the domain of the given function f(x) = (x-2)/(3-x), we need to consider any restrictions on the input values.

Restrictions on the Domain:
1. Denominator cannot be equal to zero: Since the denominator of the function is given by (3-x), we need to exclude any value of x that makes the denominator zero. Therefore, x = 3 is not included in the domain.

Domain:
The domain of the function f(x) = (x-2)/(3-x) is all the real numbers except x = 3.

Domain: (-∞, 3) ∪ (3, +∞)

Range:
The range of a function refers to the set of all possible output values (y-values) that the function can produce for the corresponding input values.

To determine the range of the given function f(x) = (x-2)/(3-x), we need to consider the possible values that can be obtained by evaluating the function for different input values.

Restrictions on the Range:
1. Division by zero: Since the function involves division, we need to ensure that the denominator is not equal to zero. Therefore, we need to exclude the value x = 3 from the range as it would result in division by zero.

Range:
The range of the function f(x) = (x-2)/(3-x) is all the real numbers except for the value y = -1.

Range: (-∞, -1) ∪ (-1, +∞)

Summary:
- The domain of the function f(x) = (x-2)/(3-x) is all real numbers except x = 3.
- The range of the function f(x) = (x-2)/(3-x) is all real numbers except y = -1.

Please note that the presentation of this answer is for explanatory purposes only and should be adapted to fit the required format.

According to me D(f)=R-{3} R(f)=R