Question

Can you guys please help with these questions I’m extremely stuck. It’s algebra 2 inverse functions.

Answer 1

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Answer:

• The graph of a function and its inverse are reflections of each other in the line y=x
• For each ordered pair (x, y) in a function, the corresponding ordered pair in the inverse function is (y, x)
• see the attachment for the tables of values

Step-by-step explanation:

Consider the function and its inverse shown in the second attachment. The function is ...

  f = {(a, 3), (b, 1), (c, 2)}

The inverse function is ...

  f^-1 = {(3, a), (1, b), (2, c)}

You will notice that the "x" and "y" of each pair are swapped between the function and its inverse. That is the point of an inverse function. It gives you the input that caused the function to create the output. For example, the pair (3, a) in the above inverse function tells you that the output 3 was the result of an input of 'a' to the original function.

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On a graph, the swapping of input and output is essentially equivalent to relabeling the axes. If we keep the same x- and y-axis labels, it is equivalent to reflecting the function graph across the line y=x. That reflection is represented by the transformation (x, y) ⇒ (y, x).

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The point of the exercise here is for you to identify some ordered pairs of one of the functions and realize that the inverse function reverses their order. You are to see that the graph of the function and its inverse are reflections of each other across the diagonal line y=x.