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Limits Continuity and Differentiability question

2020 · Shift 2 · Q23

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2020 · Shift 2 · Q23

Limits Continuity and Differentiability question

2020 · Shift 2 · Q23

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityNumerical+3 / −1

Let the functions

f:( - 1,1) \to R

and

g:( - 1,1) \to ( - 1,1)

be defined by

f(x) = |2x - 1| + |2x + 1|

and

g(x) = x - [x]

, where [x] denotes the greatest integer less than or equal to x. Let

f\,o\,g:( - 1,1) \to R

be the composite function defined by

(f\,o\,g)(x) = f(g(x))

. Suppose c is the number of points in the interval (

-

1, 1) at which

f\,o\,g

is NOT continuous, and suppose d is the number of points in the interval (

-

1, 1) at which

f\,o\,g

is NOT differentiable. Then the value of c + d is ............

Numerical answer

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