Answers: Check out the screenshot below
I filled in the boxes with the correct values.
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Explanation:
When determining the inverse, we swap the roles of x and y.
Originally, x is the input and y is the output. The inverse will swap the two and make y the input and x the output.
So in the first column of the original table we have x = 0 and y = -5. The inverse will have x = -5 and y = 0. We'll write -5 in the first box of row 1.
Then we'll have -2 in the second box of row 1 because x = 10 and y = -2 will swap to x = -2 and y = 10
This swapping process is continued until the second table is filled out completely.
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The original relation is a function because we do not have any repeated x values. Each x input leads to one and exactly one y output.
Similarly, the inverse relation is also a function. We don't have any repeated x values here either. Back in the original table, note how there aren't any repeated y values. The lack of repeated y values is sufficient to see that the inverse is a function.
The fact that neither x nor y repeats tells us that both original and inverse functions are considered one-to-one. Each x value gets is own unique y value, and vice versa.
In short, all three yes/no questions have yes as the answer.
