In general, f-1 (f (x)) = f (f-1 (x)) =

f-1 (f (x)) = f (f-1 (x)) = x

Step-by-step explanation:

Follow this simple example using the function f (x) = x + 2

f (x) = x + 2

NOw we find the inverse function f^ (1) (x).

y = x + 2

x = y + 2

y = x - 2

f^ (-1) (x) = x - 2

The inverse function is f^ (-1) (x) = x - 2

Now we do the two compositions of functions:

f^ (-1) (f (x)) = x + 2 - 2 = x

f (f^ (-1) (x)) = x - 2 + 2 = x

Both are equal to x.

Answer: f-1 (f (x)) = f (f-1 (x)) = x