One Inside Another
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 21 of 58.
A composition feeds one function's output into another function. g(f(x)) means: work out f(x), then use that result as the input of g. It reads "g of f of x", and books also write it as (g ∘ f)(x).
Take f(x) = x + 4 and g(x) = 3x, and work out g(f(2)). Inner first: f(2) is 6. Then g(6) is 18. Written out, f's rule turns the problem into g(2 + 4), then g's rule gives 3(2 + 4), and the arithmetic finishes it.
Why the inside first? g needs a number to work on, and that number is whatever f produces. Code runs the same way: in g(f(2)), the computer calls f before g has an argument.
Challenge
For f(x) = 2x + 1 and g(x) = x^2, work out g(f(1)). Use the inner rule first, then the outer one, 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