Answer:
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
