Question

Composing inverse functions use f(x)= 1/2x and f^−1(x)=2x to solve the problems.

f(2)=____, f^−1(1)=____, f^−1(f(2))=____
A) 1, 2, 1
B) 1, 1, 2
C) 2, 1, 2
D) 2, 2, 1

Answer 1

Using the given functions, we calculate f(2) as 1, then f^-1(1) as 2, and lastly use the composition of the functions to find f^-1(f(2)) equals 1. The correct answer is A) 1, 2, 1.

Step-by-step explanation:

To solve inverse functions, we'll use the given functions f(x) = ⅓x and f−1(x) = 2x. First, let's find the value of f(2).

By plugging in 2 for x in the function f(x), we get:

f(2) = ⅓ × 2 = 1

Next, we find f−1(1), which is simply:

f−1(1) = 2 × 1 = 2

Lastly, to find f−1(f(2)), we first calculate f(2) as above, then use the result as input for f−1:

f−1(f(2)) = f−1(1) = 2 × 1 = 2

The correct answer is A) 1, 2, 1, using the concepts of inverse operations and the composition of functions.