Find $( g \circ f ) ( x )$ where $f ( x ) = 4 x + 7$ and $g ( x ) = x ^ { 2 } - 1$ .
A) $4 x ^ { 3 } 28 x ^ { 2 } - 4 x - 7$
B) $4 x ^ { 2 } + 3$
C) $16 x ^ { 2 } + 56 x + 48$
D) $16 x ^ { 2 } + 6$
E) $4 x ^ { 2 } + 6$

Question

Quizplus · Accepted Answer

To find $(g \circ f)(x)$, first apply $f(x)$ and then apply $g(x)$ to the result. Substituting $f(x) = 4x + 7$ into $g(x) = x^2 - 1$, we get $g(f(x)) = (4x + 7)^2 - 1$. Expanding this gives $16x^2 + 56x + 49 - 1 = 16x^2 + 56x + 48$.

Find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) Where f(x)=4x+7f ( x ) = 4 x + 7f(x)=4x+7

Find $( g \circ f ) ( x )$ Where $f ( x ) = 4 x + 7$