Let f, g: R → R be two real valued functions defined as f(x) = \ - |x + 3|, x < 0 eˣ, x ≥ 0. and g(x) = \ x² + k₁x, x < 0 4x + k₂, x ≥ 0., where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof) (- 4) + (gof) (4) is equal to:

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jun, Morning shift · Q4207

JEE Main 202226 Jun, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

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 :