Final answer:
To find the inverse function of f(x) = 2x, we swap the variables and solve for y, resulting in f^1(x) = x/2.
Step-by-step explanation:
The question asks us to find the inverse function of f(x) = 2x. The inverse function, denoted as f^1(x), reverses the effect of the original function. To find the inverse function, we swap x and y and solve for y in the equation y = 2x.
- Replace f(x) with y: y = 2x
- Swap x and y: x = 2y
- Solve for y: y = x/2
- Replace y with f^1(x): f^1(x) = x/2
Therefore, the inverse function of f(x) = 2x is f^1(x) = x/2.