A graph of f is given. find the following:

Question

f^-1(-2)=

f^-1(6)=

Answer 1

For inverse functions, f(x) = y, whereas f^-1(y) = x, so f^-1(-2) = x where x causes f(x) = -2, in this case it is x = 2.

Doing a similar process for the other one, f^-1(6) = x where f(x) = 6, so x = 8 for this case.

Answer 2

If you know how to read the graph, you hopefully can see that f(2) = -2. It's another way we say, "What is y when x is 2?" When x = 2, y = -2, so f(2) = -2.

With the inverse, it's the reverse. f^-1(-2) means, "What is x when y is -2?" Well, we can look at our graph again and/or reverse what we just did. When y is -2, x is 2, so f^-1(-2) = 2.

It was explained to me that a function is like a machine that turns what we put in into something else. A function can be something like, "My recipe calls for 2 cup of nuts for a batch of cookies. How many batches can I make with 8 cups of nuts?" The inverse would be figuring out how many cups of nuts I used to make 3 batches. If I solve each, I get...

f(8) = 4

f^-1(3) = 6

Hope this helps!