Relations and Functions — Part 2: Composite and inverse functions: visual lesson, ISC Class 12 Mathematics

Lesson

Relations and Functions, Part 2

Do one function, then another; or undo a function completely.

In this lesson you will

The inner function acts first.

Concept

Part 2 at a glance.
You will learn to	Topic
form $f \circ g$ and $g \circ f$	composite functions
decide when a function has an inverse	invertibility
find $f^{-1}$ for algebraic functions	finding inverses
sketch $f$ and $f^{-1}$ together	graphs and $y = x$

Concept

$(f \circ g)(x) = f(g(x))$ . It is defined when the output of $g$ lies in the domain of $f$ .

(f \circ g)(x) = f\big(g(x)\big)

The inner function acts first.