If $f ( x ) = 4 x ^ { 2 } + 8 x - 9$, find and simplify $f ( 2 + x )$.
A) $4 x ^ { 2 } + 8 x - 11$
B) $23 + x$
C) $4 x ^ { 2 } + 24 x + 23$
D) $4 x ^ { 2 } + 2 x + 23$

Question

Quizplus · Accepted Answer

To find $f(2 + x)$, substitute $2 + x$ for $x$ in the given function: $f(x) = 4x^2 + 8x - 9$. This gives $f(2 + x) = 4(2 + x)^2 + 8(2 + x) - 9$. Simplifying, $f(2 + x) = 4(x^2 + 4x + 4) + 16 + 8x - 9 = 4x^2 + 16x + 16 + 16 + 8x - 9 = 4x^2 + 24x + 23$.

If f(x)=4x2+8x−9f ( x ) = 4 x ^ { 2 } + 8 x - 9f(x)=4x2+8x−9

If $f ( x ) = 4 x ^ { 2 } + 8 x - 9$