Express the function in terms of x.
-If $f ( u ) = u ^ { 5 }$ and $u = x ^ { 3 } + 8$, then express $5 u ^ { 4 } \cdot 3 x ^ { 2 }$ in terms of $x$ alone.
A) $x ^ { 2 } \left( 15 x ^ { 3 } + 8 \right) ^ { 4 }$
B) $15 \left( x ^ { 5 } + 8 \right) ^ { 4 }$
C) $15 x ^ { 2 } \left( x ^ { 3 } + 8 \right) ^ { 4 }$
D) $\left( 15 x ^ { 5 } + 8 \right) ^ { 4 }$

Question

Quizplus · Accepted Answer

Given $u = x^3 + 8$, substituting $u$ into $5u^4 \cdot 3x^2$ gives $15x^2(u)^4 = 15x^2(x^3 + 8)^4$, which matches choice C.

Express the Function in Terms of X f(u)=u5f ( u ) = u ^ { 5 }f(u)=u5

Express the Function in Terms of X $f ( u ) = u ^ { 5 }$