Question

Which tables could be used to verify that the functions they represent are inverses of each other?

Answer 1

We are asked to determine which of the tables represent the inverse function. If the function is represented by "f", then if we compose "f" with its inverse we should get:

`f(f^(-1)(x))=x`

This means that when we insert a number "x" in the function and then the result is inserted in the inverse function we should get the same value of "x". We see this happening in the first and fourth tables. for example, if we take x = -5 from the first table, then:

`f(-5)=4`

Now is we take the value 4 from the fourth table we get:

`f(4)=-5`

This is, we composed the two tables and we got the same value of "x". This happens in every value of the first and fourth tables, therefore, the two functions they represent are inverses of each other.