ACT Preparation / Unit 10 ACT 0916 worked example, 60 to 90 seconds
Evaluating a Composition
The idea
A composition is evaluated in three steps, from the inside out. First, evaluate the inner function at the given input, from its formula, table or graph. Second, use that output as the input of the outer function. Third, evaluate the outer function. For a formula of the composition, substitute the whole inner expression for x in the outer formula.
In practice
Worked example from a table: f(1) = 4, f(2) = 0, f(3) = 1; g(1) = 3, g(2) = 1, g(3) = 2. For f(g(2)): g(2) = 1, then f(1) = 4. For g(f(3)): f(3) = 1, then g(1) = 3. As a formula: if f(x) = x² and g(x) = x − 4, then f(g(x)) = (x − 4)², while g(f(x)) = x² − 4.
Where people slip
Read the table for the right function at each step. The inner output becomes an input, so look it up in the outer function's row, not the inner one's.
Your place on the trail
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Builds on
Unlocks
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