Let f, g: R → R be functions defined by f(x) = \ [x], x < 0 |1 - x|, x ≥ 0. and g(x) = \ eˣ - x, x < 0 (x - 1)² - 1, x ≥ 0. where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Evening shift · Q4151

JEE Main 202228 Jun, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let f, g : R

\to

R be functions defined by

f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x \ge 0} \cr } } \right.

and

g(x) = \left\{ {\matrix{ {{e^x} - x} & , & {x < 0} \cr {{{(x - 1)}^2} - 1} & , & {x \ge 0} \cr } } \right.

where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :

JEE Main 2022 · 28 Jun, Evening shift · Q4151

JEE Main 202228 Jun, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let f, g : R

\to

R be functions defined by

f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x \ge 0} \cr } } \right.

and

g(x) = \left\{ {\matrix{ {{e^x} - x} & , & {x < 0} \cr {{{(x - 1)}^2} - 1} & , & {x \ge 0} \cr } } \right.

where [x] denote the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :