Let \( f, g: R \rightarrow R \) be two real valued functions defined as
\[
\begin{array}{l}
f(x)...
Let \( f, g: R \rightarrow R \) be two real valued functions defined as
\[
\begin{array}{l}
f(x)=\left\{\begin{array}{cc}
-|x+3| & , \quad x0 \\
e^{x} & , \quad x \geq 0
\end{array}\right. \text { and } \\
g(x)=\left\{\begin{array}{ll}
x^{2}+k_{1} x & , \quad x0 \\
4 x+k_{2} & , \quad x \geq 0
\end{array},\right. \\
\end{array}
\]
where \( k_{1} \) and \( k_{2} \) are real constants. If ( \( \left.g \circ f\right) \) is differentiable at \( x=0 \), then \( (g \circ f)(-4)+(g \circ f)(4) \) is equal to
(a) \( 4\left(e^{4}+1\right) \)
(b) \( 2\left(2 e^{4}+1\right) \)
(c) \( 4 e^{4} \)
(d) \( 2\left(2 e^{4}-1\right) \)
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