What is the domain of the inverse of the function f(x) = (x + 2)/(x - 2)?

What is the domain of the inverse of the function f(x) = (x + 2)/(x - 2)?

• A. All real numbers
• B. All real numbers except x = 1
• C. x ≥ 0
• D. All real numbers except x = 2

Answer: (B)

To determine the domain of the inverse of the function \( f(x) = \frac{x + 2}{x - 2} \), we first need to understand the function itself and its range. The function is a rational function, and like all rational functions, it has potential restrictions in its domain. The domain of \( f(x) \) is all real numbers except where the denominator equals zero. For this function: \[ x - 2 = 0 \] This gives \( x = 2 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 2 \). Next, we need to find the range of \( f(x) \) in order to determine the domain of the inverse. As \( x \) approaches 2 from either side, \( f(x) \) approaches infinity, and as \( x \) goes to positive or negative infinity, the function approaches 1. By analyzing the function, we can conclude that it can take all real values except for 1 because there is a horizontal asymptote at \( y = 1 \). Given that the range of \( f(x) \) excludes \( y = 1 \

To determine the domain of the inverse of the function ( f(x) = \frac{x + 2}{x - 2} ), we first need to understand the function itself and its range. The function is a rational function, and like all rational functions, it has potential restrictions in its domain.

The domain of ( f(x) ) is all real numbers except where the denominator equals zero. For this function:

[

x - 2 = 0

]

This gives ( x = 2 ). Therefore, the domain of ( f(x) ) is all real numbers except ( x = 2 ).

Next, we need to find the range of ( f(x) ) in order to determine the domain of the inverse. As ( x ) approaches 2 from either side, ( f(x) ) approaches infinity, and as ( x ) goes to positive or negative infinity, the function approaches 1. By analyzing the function, we can conclude that it can take all real values except for 1 because there is a horizontal asymptote at ( y = 1 ).

Given that the range of ( f(x) ) excludes ( y = 1 \