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Composition is a binary operation like addition, subtraction, multiplication and division are binary operations. (meaning they operate on two elements) f+g f-g fgfg The composition symbol is: Thus

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The easiest way to describe composition is to say it is like substitution. In fact Read f of g of x which means substitute g(x) for x in the f(x) expression.

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For example: Suppose f(x)= 2x + 3, and g(x) = 8 - x Then Means substitute the g function for x in the f function… like this f(x)= 2x + 3 f(g(x) )= 2 g(x) + 3

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f(x)= 2x + 3, and g(x) = 8 - x f(x)= 2x + 3 f(g(x) )= 2 g(x) + 3 Now substitute what g equals for g(x) f(8 - x)= 2 (8 - x) + 3 = 16 - 2x + 3 = 19 - 2x So, = 19 - 2x

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An interesting fact is that most of the time. Let’s see if this is the case for the previous example.

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f(x) = 2x + 3, andg(x) = 8 - x Thus we will substitute f into g. g(x) = 8 - x g(f(x) ) = 8 - f(x) Now substitute what f(x) is: g(2x + 3) = 8 - (2x + 3) = 8 - 2x - 3 = 5 - 2x

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Let and

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Write the f function Substitute g(x) for x Replace g(x) with Simplify Step 1 Step 2 Step 3 Step 4

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Find: When ready click your mouse. The answer is: A) B) Move your mouse over the correct answer.

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Find: When ready click your mouse. The answer is: B) A) Move your mouse over the correct answer.

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Find: When ready click your mouse. The answer is: B) A) Move your mouse over the correct answer.

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A) Ans. A for the previous example Was actually

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1.3 New functions from old functions: Transformations.

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