To determine the correct ordered pair for the inverse of the function [tex]\( f(x) \)[/tex], let's first understand the relationship between a function and its inverse.
Given that [tex]\( (2, 1) \)[/tex] is an ordered pair of the function [tex]\( f(x) \)[/tex], this means that when [tex]\( x = 2 \)[/tex], the function [tex]\( f \)[/tex] produces [tex]\( y = 1 \)[/tex]. This can be written mathematically as:
[tex]\[ f(2) = 1 \][/tex]
Now, for the inverse function [tex]\( f^{-1}(x) \)[/tex], the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are swapped. Therefore, if [tex]\( f(2) = 1 \)[/tex], then for the inverse function:
[tex]\[ f^{-1}(1) = 2 \][/tex]
In terms of ordered pairs, this means for the inverse function [tex]\( f^{-1}(x) \)[/tex], the pair [tex]\( (y, x) \)[/tex] will be:
[tex]\[ (1, 2) \][/tex]
Thus, the correct ordered pair for the inverse of [tex]\( f(x) \)[/tex] is [tex]\( (1, 2) \)[/tex].
Looking at the answer choices given:
A. [tex]\((1,1)\)[/tex]
B. [tex]\((1,2)\)[/tex]
C. [tex]\((2,1)\)[/tex]
D. [tex]\((2,2)\)[/tex]
The ordered pair that must be an ordered pair of the inverse of [tex]\( f(x) \)[/tex] is:
[tex]\[ \boxed{(1, 2)} \][/tex]
