Let the functions f: R → R and g: R → R be defined as: f(x) = \ x + 2, x < 0 x², x ≥ 0. and g(x) = \ x³, x < 1 3x - 2, x ≥ 1. Then, the number of points in R where (fog) (x) is NOT differentiable is equal to:

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 16 Mar, Morning shift · Q4200

JEE Main 202116 Mar, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let the functions f : R

\to

R and g : R

\to

R be defined as :

f(x) = \left\{ {\matrix{ {x + 2,} & {x < 0} \cr {{x^2},} & {x \ge 0} \cr } } \right.

and

g(x) = \left\{ {\matrix{ {{x^3},} & {x < 1} \cr {3x - 2,} & {x \ge 1} \cr } } \right.

Then, the number of points in R where (fog) (x) is NOT differentiable is equal to :