This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
here's how to find f(f^-1(x)) for f(x) = x - (2)/(3): First, we need to find the inverse function f^-1(x). Step 1: Replace f(x) with y. y = x - (2)/(3) Step 2: Swap x and y. x = y - (2)/(3) Step 3: Solve for y. Add (2)/(3) to both sides: y = x + (2)/(3) Step 4: Replace y with f^-1(x). f^-1(x) = x + (2)/(3) Now, we find f(f^-1(x)) by substituting f^-1(x) into f(x). Step 5: Substitute f^-1(x) into f(x). Given f(x) = x - (2)/(3), we replace x with f^-1(x): f(f^-1(x)) = f(x + (2)/(3)) f(x + (2)/(3)) = (x + (2)/(3)) - (2)/(3) f(x + (2)/(3)) = x + (2)/(3) - (2)/(3) f(x + (2)/(3)) = x The result is: ff^-1(x) = x What's next? Send 'em!