JEE Main 2026 — Apr 4, Shift 2 — Mathematics solution

JEE Main2026Apr 4, Shift 2Mathematics

Let $f (x) = {e^{x - 1}, x < 0 x^{2} - 5 x + 6, x \geq 0$ and $g (x) = f (∣ x ∣) + ∣ f (x) ∣$ . If the number of points where $g$ is not continuous and is not differentiable are $α$ and $β$ respectively, then $α + β$ is equal to ______

Your answer

Solution

Graph of $f (x)$

Now graph of $f (∣ x ∣)$

$f (∣ x ∣)$ is continuous function and it is non diff. at $x = 0$

Graph of $∣ f (x) ∣$

$∣ f (x) ∣$ is discontinuous at $x = 0$

$∣ f (x) ∣$ is non-diff. at $x = 0, 2, 3$

$g (x) = f (∣ x ∣) + ∣ f (x) ∣$

$g (x)$ will be discontinuous at $x = 0$

$g (x)$ will be non diff at $x = 0, 2, 3$

$α = 1, β = 3$

$α + β = 1 + 3 = 4$

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