The table below shows some inputs and outputs of the invertible function f with domain all real numbers.

x | 14 | -6 | -1 | 10 | -10 | 3
f(x) | 7 | -10 | -15 | 14 | -4 | -9

Find the following values:

f^-1(f^-1(7)) = ?
f^-1(-4) = ?

Answer for the first box = 10

Answer for the second box =  -10

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Work Shown:

f(x) is a function where we plug in the given row of x values to have them lead to the corresponding f(x) values in the table. We see that x = 14 leads to y = f(x) = 7. Going backwards, we can say . The inverse simply undoes everything f(x) does.

So,

For the portion , look at the column that has x = 10. This shows it leading to f(x) = 14. You trace this column upward to go backward to undo f(x).

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That takes care of the first part. The second part is pretty much the same idea. We locate where -4 is in the bottom row, and then we write down the corresponding x value.

We see that y = -4 pairs with x = -10, which is why

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Keep in mind that this function must be one-to-one for the inverse to exist. If not, then you'll have to do some kind of domain restriction.

7.3

step-by-step explanation: