Question

Use f(x) = 1/2x and f -1(x) = 2x to solve the problems.
f(2)=?
f⁻¹=?
f⁻¹(f(2))=?

Answer 1

The solution involves finding f(2) by substituting '2' into the function f(x), resulting in 1. The inverse function f-1(x) doesn't have a direct numerical answer without a specific input. Finally, the value of f-1(f(2)) is found by applying the inverse function to the result of f(2), giving us 2.

Step-by-step explanation:

The student’s question involves evaluating a function and its inverse, with the given function f(x) = 1/2x and its inverse f-1(x) = 2x. To solve for f(2), we simply substitute '2' into the function f(x):

f(2) = 1/2(2) = 1

Next, the inverse function f-1(x) = 2x can be referred to in answering further questions, but 'f-1' as given doesn't have a direct numerical answer without a specific input value, much like how asking for 'f' alone doesn't have a specific numerical answer.

Then, we evaluate the composite f-1(f(2)) by first finding f(2), as we did above, which is 1. Now we input this result into the inverse function:

f-1(f(2)) = f-1(1) = 2(1) = 2

This demonstrates that applying the function and then its inverse brings us back to the original value we started with, which is a defining property of inverse functions.