Respuesta :

mathstudent55

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

abidemiokin

The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

We are to prove the relationship;

[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]

To get the unknown, let f(x) = x - 2

Find its inverse:

Let y = x - 2

Replace y with x;

x = y - 2

y = x+2

Hence [tex]f^{-1}x = x+2[/tex]

Next is to get [tex]f(f^{-1}(x))[/tex]

[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]

We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

Learn more here: https://brainly.com/question/12220962

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