Understanding Algebraic Inverses Lesson 1.06

Finding Inverse Functions Algebraically

Ever wonder how to reverse a mathematical operation? That's exactly what inverse functions do! To find an inverse function algebraically, you need to swap the variables x and y and then solve for y.

The process follows four simple steps: First, rewrite the original function as y = f$x$. Second, switch the positions of x and y in the equation. Third, solve the new equation for y using inverse operations. Finally, rewrite your answer as f^-1$x$.

Let's see this in action with two examples. For f$x$ = 5/$x-2$, after swapping x and y and solving, we get f^-1$x$ = 5/x + 2. Similarly, for f$x$ = ∛$2x+5$, the inverse function is f^-1$x$ = $x³-5$/2.

Pro Tip: Remember that the inverse operation of a root is a power! When dealing with cube roots in your original function, you'll need to cube both sides when finding the inverse.