Question

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)

Answer 1

Answer:

$f(x) = |2\cdot x^{2}+x|$ and $g(x) = x+1$

Step-by-step explanation:

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