JEE PYQ: Continuity And Differentiability Question 3
Question 3 - 2021 (16 Mar Shift 2)
Let $f : \mathbb{R} \to \mathbb{R}$ and $g : \mathbb{R} \to \mathbb{R}$ be defined as
$$f(x) = \begin{cases} x + a, & x < 0 \ |x - 1|, & x \geq 0 \end{cases} \quad \text{and} \quad g(x) = \begin{cases} x + 1, & x < 0 \ (x - 1)^2 + b, & x \geq 0 \end{cases}$$
where $a, b$ are non-negative real numbers. If $(g \circ f)(x)$ is continuous for all $x \in \mathbb{R}$, then $a + b$ is equal to ______.
BETA
