Let f, g : R →R be two real valued functions defined as f(x) = {-|x + 3|, x < 0, e^x, x ≥ 0 and g(x) = {x^2+k1x, x < 0

Question

Let f, g : R →R be two real valued functions defined as 

\(f(x)=\begin{cases}-|x+3|&,x<0\\e^x&,x\ge 0\end {cases}\) and g(x) = \(\begin{cases}x^2+k_1x&,x <0\\4x + k_2&,x \ge 0\end{cases},\)where k₁ and k₂ are real constant. If (gof) is differentiable at x = 0, then (gof) (-4) + (gof) (4) is equal to:

(A) 4(e⁴ + 1)

(B) 2(2e⁴ + 1)

(C) 4e⁴

(D) 2(2e⁴ - 1)

Answer 1

Correct answer is (D) 2(2e⁴ – 1)