f,g:R→R be two real valued function defined as fx=-x+3,x<0ex,x≥0 and gx=x2+k1x,x<04x+k2,x≥0, where k1 and k2 are real constants. If gof is differentiable at x=0, then gof-4+gof4 is equal to

Question

f, g : R \to R

be two real valued function defined as

f (x) = \{\begin{matrix} - |x + 3| & , & x < 0 \\ e^{x} & , & x \geq 0 \end{matrix}

and

g (x) = \{\begin{cases} x^{2} + k_{1} x & , & x < 0 \\ 4 x + k_{2} & , & x \geq 0 \end{cases}

, where

k_{1}

and

k_{2}

are real constants. If

g o f

is differentiable at

x = 0

, then

g o f (- 4) +

g o f (4)

is equal to

4 (e^{4} + 1)

2 (2 e^{4} + 1)

4 e^{4}

2 (2 e^{4} - 1)

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