Final Answer:
The tables that could be used to verify that the functions they represent are inverses of each other are options a) and e). Thus the correct option is a.x(-5,-3,0,2,4),y(4,0,-6,-10,-14), e.x(-5,-3,0,2,4),y(-4,0,6,10,14)
Step-by-step explanation:
In option a), the given tables represent two functions, let's call them f(x) and g(x). The first column represents the input values (x) for function f(x), and the second column represents the corresponding output values (y) for f(x). In the second table, the input values for function g(x) are in the first column, and the corresponding output values are in the second column. To check if functions f(x) and g(x) are inverses, you should verify that when you input the output values of f(x) into g(x) and vice versa, you get back to the original input values. If this holds true for both tables, the functions are inverses.
Similarly, in option e), the given tables represent two functions. The process is the same – you need to check whether inputting the output values of one function into the other gives you the original input values. If this holds true for both tables, the functions are inverses.
It's important to note that for two functions to be inverses, the composition of the functions (f(g(x)) and g(f(x))) should result in x. So, for option a), check that f(g(x)) = x and g(f(x)) = x for the given values in the tables. Repeat the process for option e) as well.
Therefore, the correct option is a.x(-5,-3,0,2,4),y(4,0,-6,-10,-14), e.x(-5,-3,0,2,4),y(-4,0,6,10,14)