Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
To determine if f(x) and g(x) are inverses of each other:
If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
[tex]\implies f(2)=2(2)+5=9[/tex]
Substitute x = 9 into g(x):
[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
