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Limits Continuity and Differentiability question

2022 · 26 Jun · Shift 1 · Q26

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 26 Jun · Shift 1 · Q26

Limits Continuity and Differentiability question

2022 · 26 Jun · Shift 1 · Q26

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let f, g : R

\to

R be two real valued functions defined as

f(x) = \left\{ \begin{matrix} -|x + 3| & , & x \lt 0 \\ e^x & , & x \ge 0 \end{matrix} \right.

and

g(x) = \left\{ \begin{matrix} x^2 + k_1 x & , & x \lt 0 \\ 4x + k_2 & , & x \ge 0 \end{matrix} \right.

, where

k_1

and

k_2

are real constants. If (gof) is differentiable at x = 0, then (gof)(

-

4) + (gof)(4) is equal to :

A
$4({e^4} + 1)$
B
$2(2{e^4} + 1)$
C
$4{e^4}$
D
$2(2{e^4} - 1)$

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