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Composition of Functions

(f*g)(x) and (g*f)(x)

f(x)=x-4 and g(x)=3x-4

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Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
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Given:     f(x) = x - 4          and          g(x) = 3x - 4

(fοg)(x) = f(g(x))

            = f(3x - 4)              replace every x in f(x) with '3x - 4'

            = (3x - 4) - 4

            = 3x - 4 - 4

            = 3x - 8

(gοf)(x) = g(f(x))

            = g(x - 4)                  replace every x in g(x) with 'x - 4'

            = 3(x - 4) - 4

            = (3·x - 3·4) - 4

            = 3x - 12 - 4

            = 3x - 16