For the given functions f and g , find the indicated composition.
-$f ( x ) = 4 x ^ { 2 } + 2 x + 3 , \quad g ( x ) = 2 x - 4$ $( g \cdot f ) ( x )$
A) $4 x ^ { 2 } + 2 x - 1$
B) $8 x ^ { 2 } + 4 x + 10$
C) $8 x ^ { 2 } + 4 x + 2$
D) $4 x ^ { 2 } + 4 x + 2$

Question

Quizplus · Accepted Answer

The composition $(g \cdot f)(x)$ means applying $g$ to the result of $f(x)$, which is $g(f(x))$. Substituting $f(x) = 4x^2 + 2x + 3$ into $g(x) = 2x - 4$, we get $g(f(x)) = 2(4x^2 + 2x + 3) - 4 = 8x^2 + 4x + 6 - 4 = 8x^2 + 4x + 2$.

For the Given Functions F and G , Find the Indicated