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How to Multiply Composite Functions

Students typically encounter multiplying composite functions in precalculus and calculus courses. Much like adding and subtracting composite functions, in order to solve multiplication of composite functions, start with recording and solving for the given information.

Instructions

    • 1

      Solve for f(x) and g(x) individually. You may have other variables rather than "f" and "g," but the process would still be the same.

    • 2

      Multiply the two solutions derived from solving each individual function.

    • 3

      Consider the following practice problem: f(x) = 3x and g(x) = 5x + 2. What is f(8) times g(2)? The first step to solving this problem is substituting the 9 with the "x" in the function f(x), so f(8) = 3(8) = 24. Solving for g(2) yields g(2) = 5(2) + 2 = 12. Complete the problem by multiplying 24 x 12 = 288.

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