Composition of Functions
Composition feeds one function's output into another: in f(g(x)), the inner g acts on x first and f acts on the result. The circle notation writes f first but runs g first, order genuinely matters ((x + 3) squared is not x squared + 3), and the domain of a composition is policed by both gates: x must be legal for the inner function, and the inner output must be legal for the outer one.
The mistakes are order mistakes in different clothes: running the outer function first, stopping at the inner output, reading the composition as a product, or trusting left-to-right reading over inside-out reading. The lesson drills the two-lookup discipline on tables and formulas until the middle step is automatic.
The work
3 ways in · any order
Lesson
Composition of Functions
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Inside acts first: the lesson drills the two-lookup discipline for tables, substitution for formulas, the domain gates a composition must clear, and decomposition for the functions this unit inverts next. Ten scenarios close it out, every distractor a wrong order in disguise.
Diagnostic
10-item topic check
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Ten items spanning the Topic 2.7 misconception in its main costumes: outer-first evaluation, stopping at the inner output, composition read as multiplication, and assuming f of g equals g of f. The bank ships with the Unit 2 data drop.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.