How to Find Inverse Functions Definition, Types, Examples & Uses

How to Find Inverse Functions

Subject: Mathematics

Book: Maths Mastery

An inverse function f⁻¹ swaps inputs and outputs of f: if y=f(x), then x=f⁻¹(y). Graphically, it reflects f across the line y=x. To find an inverse, replace f(x) with y, then solve for x in terms of y, and rename x as f⁻¹(y). For instance, y=2x+3 → x=(y–3)/2 → f⁻¹(x)= (x–3)/2. Inverse functions are crucial in algebraic transformations, “undoing” processes (like logs vs. exponentials), or solving equations about rates/time. Checking domain/range restrictions ensures the inverse is valid, reinforcing your function-centric problem-solving repertoire.