Inverse Function

What is Inverse Function?

The inverse of a one-one function f, written f inverse, is the function that reverses the mapping: if f sends a to b then f inverse sends b back to a. It exists only when f is one-one over its stated domain, its domain is the range of f, and its range is the domain of f.

This definition is part of the Functions chapter in Cambridge IGCSE Additional Mathematics.

Concepts related to Inverse Function

• one-one
• range
• restricted domain

Common mistakes with Inverse Function

• “Every function has an inverse; I just have to find it.” Correct Only a one‑one function has an inverse function. \(f(x)=x^{2}\) on \(\mathbb{R}\) has none, because \(f(2)=f(-2)=4\). Restricting the domain to \(x\ge 0\) is what makes an inverse possible.