Question

what is the inverse of f(x)= x - 5

Answer 1

\[y = x- 5\]Replace \(y\) with \(x\) and vice-versa.\[x = y - 5\]\[\Rightarrow x + 5 = y\]Now replace \(y\) back with \(f(x)\)\[f(x) = x + 5\]Now that's our inverse function. It's not good practice to use \(f(x)\) for the inverse too. So call it \(f^{-1}(x)\).\[f^{-1}(x) = x + 5\]