Inverse Functions (Edexcel A-Level Mathematics): Flashcards

It must be one-to-one (1-to-1).

$f(x) = x^2$, $x \in \mathbb{R}$ has no inverse.

Restrict to a one-to-one portion of the function.

$f^{-1}(x) = \sqrt{x}$.

Swap $x$ and $y$, then rearrange to find $y$.

$f^{-1}(x) = \ln(x)$.

Range is $f(x) > 0$.

$f^{-1}(x) = (x - 3)/2$.

The $x$ and $y$ coordinates are swapped to find its inverse.

They intersect at $(k, k)$ where $f(k) = k$.