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Which pair of functions represents a decomposition of f(g(x)) = | 2(x + 1)2 + (x + 1) | ? f(x) = (x + 1)2 and g(x) = | 2x + 1 | f(x) = (x + 1) and g(x) = | 2x2 + x | f(x) = | 2x + 1 | and g(x) = (x + 1)2 f(x) = | 2x2 + x | and g(x) = (x + 1)

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xero099

Answer:

[tex]f(x) = |2\cdot x^{2}+x|[/tex] and [tex]g(x) = x+1[/tex]

Step-by-step explanation:

Let [tex]f \circ g\, (x) = |2\cdot (x+1)^{2}+(x+1)|[/tex], a composition consist in replacing the variable of the first function ([tex]f(x)[/tex]) with the second function ([tex]g(x)[/tex]). By observation, it is quite evident that [tex]g(x) = x+1[/tex], whereas [tex]f(x) = |2\cdot x^{2}+x|[/tex].

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