AP Calculus AB/BC

Nov 29, 2025

1 page

Understanding Algebraic Inverses Lesson 1.06

Ciayni Langley @yani_us

Inverse functions are a powerful mathematical tool that let you "undo" what a function does. When you understand... Show more

1.06- Inverse Functions Algebraically 9/6
Algebraically, you can obtain f-'(x) from f(x) by swapping xay.
Ex 1: If f(x) = 5₂, find f'(x) | E

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.

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AP Calculus AB/BC

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Nov 29, 2025

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1 page

Understanding Algebraic Inverses Lesson 1.06

Ciayni Langley

@yani_us

Inverse functions are a powerful mathematical tool that let you "undo" what a function does. When you understand inverse functions algebraically, you'll be able to work backward from a function's output to find its input—a skill that's essential for solving... Show more

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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).

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.