Question

Composing Inverse Functions

Use f(x) = 2 x and f-1(x) = 2x to solve the problems.
f11-2)=
X =
f(2)=
fl-4)=
f1 (1) =
ff1(-2)) =
f|(2)) =
In general, f '(F(x)) = f(F-1(x)) =1

Answer 1

To solve the problems using the functions f(x) = 2x and f^{-1}(x) = 2x, you can follow the step-by-step process below.

Step-by-step explanation:

An inverse function is a function that undoes the effect of another function. In this case, we have f(x) = 2x and f^{-1}(x) = 2x. To solve the problems using these functions:

1. f^{-1}(x) = f(11) = f(2) = 2(11) = 22
2. f^{-1}(x) = f(-4) = f(2) = 2(-4) = -8
3. f^{-1}(x) = f(1) = 2(1) = 2
4. f(f^{-1}(-2)) = f(2) = 2(2) = 4
5. f(f^{-1}(2)) = f(2) = 2(2) = 4 (this is the identity property)

In general, the derivative of f composed with its inverse function is equal to 1.