Question

If f(x) = x + 4 and g(x) = x ^ 2 - 1 , what is big(g f big) big(x big) ?

Answer 1

Given

$\begin{gathered} f\mleft(x\mright)=x+4 \\ g\left(x\right)=x^2-1 \end{gathered}$

Find

$(g\circ f)(x)$

Explanation

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ (g\circ f)(x)=g(x+4) \\ (g\circ f)(x)=(x+4)^2-1 \\ (g\circ f)(x)=x^2+16+8x-1 \\ (g\circ f)(x)=x^2+8x+15 \end{gathered}$

Final Answer

Therefore , the correct option is C.