What is an Inverse Function?
An inverse function reverses the effect of the original function.
If a function takes x to y, then its inverse takes y back to x.
👉 f(x) = y ⇒ f⁻¹(y) = x
So, inverse function "undoes" the original function.
Condition for Inverse
Not every function has an inverse.
- Function must be one-one (injective)
- Function must be onto (surjective)
👉 Function must be bijective (both one-one and onto)
Steps to Find Inverse
- Step 1: Write y = f(x)
- Step 2: Replace f(x) with y
- Step 3: Swap x and y
- Step 4: Solve for y
- Step 5: Write y = f⁻¹(x)
Step-by-Step Example
Find inverse of f(x) = 2x + 3
- Step 1: y = 2x + 3
- Step 2: Swap → x = 2y + 3
- Step 3: Solve → y = (x - 3)/2
👉 f⁻¹(x) = (x - 3) / 2
Understanding with Diagram
Function and its inverse reverse each other.
Key Points to Remember
- Inverse reverses the function
- Exists only for bijective functions
- Graph of inverse is reflection in line y = x