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Explanation:
g(x) is the inverse of f(x), which tells us that g undoes everything f(x) does.
If we input x = -6 then f(x) outputs 1
g(x) then reverses this to say that g(1) = -6. The inputs and outputs swap roles.
Moving to row 2, we see that f(-3) = 2 which reverses to g(2) = -3
We'll replace the g(2) with -3 to go from
f( g(2) )
to
f( -3 )
-3 isn't the answer, but I wanted to put it in bold to show how the replacement is happening.
From the table, we see that f(-3) = 2 which is the final answer
In other words, f(g(2)) = 2
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Side note:
We can say that f(g(x)) = x for any number x in the domain of g(x).
As another example, g(3) = 5 and f(g(3)) = f(5) = 3.
The same works the other way around meaning that g(f(x)) = x.