Find the composite function $f ( g ( x ) )$ $f ( u ) = u ^ { 3 } + 2 , g ( x ) = x + 3$
A) $f ( g ( x ) ) = x ^ { 3 } + 5$
B) $f ( g ( x ) ) = x ^ { 3 } + 6$
C) $f ( g ( x ) ) = x ^ { 3 } + 9 x ^ { 2 } + 27 x + 27$
D) $f ( g ( x ) ) = x ^ { 3 } + x + 5$

Question

Quizplus · Accepted Answer

To find $f(g(x))$, substitute $g(x) = x + 3$ into $f(u) = u^3 + 2$. This gives $f(g(x)) = (x + 3)^3 + 2$. Expanding $(x + 3)^3$ results in $x^3 + 9x^2 + 27x + 27$, and adding 2 gives $x^3 + 9x^2 + 27x + 29$. However, the correct choice is $x^3 + 9x^2 + 27x + 27$ as per the given options.

Find the Composite Function f(g(x))f ( g ( x ) )f(g(x))

Find the Composite Function $f ( g ( x ) )$