Let f, g : R $\to$ R be two real valued functions defined as $$f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$, where k1 and k2 are real constants. If (gof) is differentiable at x = 0, then (gof) ($-$$ 4) + (gof) (4) is equal to :

Question

Let f, g : R $\to$ R be two real valued functions defined as $$f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$, where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof) ($-$$ 4) + (gof) (4) is equal to :

$4({e^4} + 1)$

$2(2{e^4} + 1)$

$4{e^4}$

$2(2{e^4} - 1)$

Solution

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