Respuesta :
The pair of functions which are inverses of each other from the provided function is given in option A and B. Option A and B is correct.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
When a function has the point (x,y), then the inverse of this function has the points (y,x).
[tex](x,y)^{-1}=(y,x)[/tex]
For example, if a function has point (1,2). Then its inverse has the points (2,1).
The first pair of function given in the problem is,
[tex]f(x)={(-5.-9).(-3,-4), (0, 1), (3, 7), (6, 13)}\\g(x) = {(-9,-5),(-4,-3), (1.0), (7,3), (13,6)}[/tex]
In this pair, each point of function g(x) is an inverse of the respective point of function f(x).
In the second pair, the function is given as,
[tex]f(x) = x +7[/tex]
Let, f(x) as y,
[tex]y = x +7[/tex]
Change the points of x and y
[tex]x = y +7\\x-7=y\\y=x-7[/tex]
Put f(x) on place of y,
[tex]f(x) = x -7[/tex]
This is equal to the function g(x)=x-7. Thus, the functions are inverse. In the third pair, the inverse of the f(x) is not equal to the g(x).
Thus, the pair of functions which are inverses of each other from the provided function is given in option A and B. Option A and B is correct.
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