Answer:
13
Explanation:
You want the sum of f^-1(-7) and f(-7) given the function definition in the table.
Inverse function
The inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...
(x, f^-1(x)) ≡ (f(x), x)
Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:
f^-1(-7) = 6 . . . . . from the 4th column of the table
Function value
We can read the function value directly from the table:
f(-7) = 7 . . . . . . the first column of the table
Sum
Then the sum of interest is ...
f^(-1)(-7) +f(-7) = (6) +(7)
f^(-1)(-7) +f(-7) = 13
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Additional comment
The inverse function ordered pairs are ...
(x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}