The function f(x) = \ (π)/4 + tan ⁻¹x, | x | ≤ 1 1/2(| x | - 1), | x | > 1. is:

(D) continuous on R–1 and differentiable on R––1, 1

(A) continuous on R––1 and differentiable on R––1, 1

(B) both continuous and differentiable on R–1

(C) both continuous and differentiable on R––1

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 4 Sep, Evening shift · Q4195

JEE Main 20204 Sep, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

The function

f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.

is :

JEE Main 2020 · 4 Sep, Evening shift · Q4195

JEE Main 20204 Sep, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

The function

f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.

is :