Question

In general, f−1(f(x)) = f(f−1(x)) =

Answer 1

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

Answer 2

Answer:

Use f(x) = 1

2

x and f -1(x) = 2x to solve the problems.

Part 1...

f(2) =

1

f−1(1) =

2

f−1(f(2)) =

2

Part 2...

f−1(−2) =

⇒ -4

f(−4) =

⇒ -2

f(f−1(−2)) =

-2

Part 3..

In general, f−1(f(x)) = f(f−1(x)) =

x

Step-by-step explanation: