The inverse function of f(x) = (x + 4)/2 is f^(-1)(x) = 2x - 4. Verification of inverse relationships, f(f^(-1)(x)) = x and f^(-1)(f(x)) = x, confirms their status as inverses.
To find the inverse of the function f(x) = (x + 4)/2, follow these steps:
Replace f(x) with y: y = (x + 4)/2.
Swap x and y: x = (y + 4)/2.
Solve for y: Multiply both sides by 2 to eliminate the fraction and isolate y.
2x = y + 4 implies y = 2x - 4.
Replace y with f^(-1)(x): f^(-1)(x) = 2x - 4.
So, the inverse function of f(x) is f^(-1)(x) = 2x - 4. Verify this by confirming that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x, indicating the functions are inverses.