Functions and Graphs

Functions are typically denoted as $f(x)$, where $x$ is the input value.

• Domain: All possible values for $x$ (inputs).
• Range: All possible values for $f(x)$ (outputs).

An inverse function, denoted $f^{-1}(x)$, reverses the action of $f(x)$.

If $f(a) = b$, then $f^{-1}(b) = a$.

To find the inverse algebraically:

1. Replace $f(x)$ with $y$.
2. Swap $x$ and $y$.
3. Solve for $y$.