Question

values for relation g are given in the table which ordered pair is in g inverse

a. (13,5)
b. (4,9)
c. (-2,-2)
d. (-3,-5)

Answer 1

According to given table for Relation g, we have following order pairs

(2,2)

(3,5)

(4,9)

(5,13)

Note: Each of first value in coordinate is x and each of the second value in the coordinate is y value.

We need to check the option, which gives an order pair of inverse relation of g.

In order to find inverse relation of a coordinate, we need to switch x and y values of a coordinate.

x value goes in y place and y value goes in x place.

So, the order pairs of inverse relation of given relation of g can be written as  

(2,2) --> (2,2)

(3,5) --> (5,3)

(4,9) --> (9,4)

(5,13) --> (13,5).

In the given options, we have first order pair (13,5), which is the inverse of order pair (5,13).

Therefore, correct option is first option (13,5)

Answer 2

A function g(x) tells the value of the function based on the value of x.

In the table in the figure we can see that when x = 2 then g = 2, when x = 3 then g = 5, when x = 4 then g = 9, when x = 5 then g = 13.

Inverse of a function tells the x-value when the function's value for that particular x is given.

Hence, in inverse of function g, the x and y values will interchange from the table.

So inverse of the g function will be represented by the pair (2,2) or (5,3) or (9,4) or (13,5).

Option A is (13,5) , which we have indicated above that it represents inverse of g.

Hence, option A is the correct answer.