Let f: R → R and g: R → R be defined as f(x) = \ x + a, x < 0 |x - 1|, x ≥ 0. and g(x) = \ x + 1, x < 0 (x - 1)² + b, x ≥ 0., where a, b are non-negative real numbers. If (gof) (x) is continuous for all x R, then a + b is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 16 Mar, Evening shift · Q42

JEE Main 202116 Mar, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R and g : R

\to

R be defined as

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

and

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

, where a, b are non-negative real numbers. If (gof) (x) is continuous for all x

\in

R, then a + b is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Limit, Continuity and Differentiability Question with Answer (16 Mar Evening shift, Q42) | JEE Arc