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Composition of Functions

Composition of Functions. Definition of Composition of Functions. The composition of the functions f and g are given by (f o g)(x) = f(g(x)). (f o g)(x) is read as. f composed of g. Steps in computing (f o g)(x).

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Composition of Functions

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  1. Composition of Functions

  2. Definition of Composition of Functions The composition of the functions f and g are given by (f o g)(x) = f(g(x))

  3. (f o g)(x) is read as f composed of g

  4. Steps in computing (f o g)(x) 1. Begin with the f function.2. Plug the g formula in for x.3. Complete the f formula.4. Reduce the equation.

  5. Supposef (x) = x2 + 3g(x) = 4x

  6. (f o g) (x) = f(g(x))Plug the g formula in for x in the f formula f(4x) = (4x)2 + 3 = 16x2 + 3

  7. (g o f) (x) = g(f(x))Plug the f formula in for x in the g formula g(x2 +3) = 4(x2 + 3) = 4x2 + 12

  8. Recall f(x) = x2 + 3 and g(x) = 4x (g o f)(0) = g(f(0)) = g(3) = 12 0 f(x) = x2 + 3 3 g(x) = 4x 12

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