Answer:
Explanation:
To find the inverse function of f(x) = x/2, we need to interchange the roles of x and y and solve for y.
Step 1: Replace f(x) with y.
y = x/2
Step 2: Swap x and y.
x = y/2
Step 3: Solve for y.
Multiply both sides of the equation by 2 to isolate y.
2x = y
Step 4: Replace y with f^(-1)(x) to represent the inverse function.
f^(-1)(x) = 2x
Therefore, the inverse function of f(x) = x/2 is f^(-1)(x) = 2x.
To verify this, we can apply the inverse function to the original function. If we plug in f^(-1)(x) = 2x into f(x), we should get x as the result.
f(f^(-1)(x)) = f(2x) = (2x)/2 = x
As we can see, applying the inverse function to the original function yields the input x. This confirms that f^(-1)(x) = 2x is indeed the inverse function of f(x) = x/2.