A Function of Itself
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 23 of 58.
A function can be composed with itself. h(h(x)) means: apply h, then apply h again to the output. Take h(x) = 3x - 1 and work out h(h(1)). First h(1) is 2. Then h(2) is 5.
Written out, the inner call comes first and gives h(3(1) - 1), the outer one 3(3(1) - 1) - 1, and the arithmetic finishes it: 3(2) - 1, then 5.
Do not confuse this with squaring or doubling. (h(1))^2 is 4 and 2h(1) is 4, but h(h(1)) is 5. Applying a rule twice means running the second pass on the first pass's output, the way a loop feeds each result back in.
Challenge
For f(x) = 2x - 3, work out f(f(2)). Tap Use f(x) = ... twice, the inner call first, then type the arithmetic line by line.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories2Expressions as Inputs
A Letter as InputA Sum as InputShifting the InputSolving f(x) = kRecap: Inputs as Expressions5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip