Let the functions $f:R \to R$ and $g:R \to R$ be defined as $f(x) = \left\{ {\begin{array}{*{20}{c}} {x + 2,}&{x\,\, < \,\,0}\\ {{x^2},\,}&{x\,\, \ge \,\,0} \end{array}} \right.\,$ and $g(x) = \left\{ {\begin{array}{*{20}{c}} {{x^3},}&{x\,\, < \,\,1}\\ {3x - 2,}&{x\,\, \ge \,\,1} \end{array}} \right.\,$ Then, the number of points in $R$ where $(fog)\,(x)$ is NOT differentiable is equal to :

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

Let the functions

f:R \to R

and

g:R \to R

be defined as

f(x) = \left\{ {\begin{array}{cccccccccccccccccccc} {x + 2,}&{x\,\, < \,\,0}\\ {{x^2},\,}&{x\,\, \ge \,\,0} \end{array}} \right.\,

and

g(x) = \left\{ {\begin{array}{cccccccccccccccccccc} {{x^3},}&{x\,\, < \,\,1}\\ {3x - 2,}&{x\,\, \ge \,\,1} \end{array}} \right.\,

Then, the number of points in

R

where

(fog)\,(x)

is NOT differentiable is equal to :

View answer and explanation

Correct option: A

Option A (1) is correct because the function (fog)(x) is non-differentiable at only one point, x = 0, due to discontinuity.