JEE Main 2022 Mathematics question
f, g : ℝ ℝ be two real valued functions defined as f(x) = −|x + 3| for x < 0 and for , and for x < 0 and for , where and are real constants. If (g∘f) is differentiable at x = 0, then (g∘f)(−4) + (g∘f)(4) is equal to :
Answer: (4)
Solution
For x < 0, f(x) = −|x + 3| = −(x + 3) near 0, so = −3, while . Continuity of g∘f at 0 needs g(−3) = g(1): . Differentiability needs equal derivatives: for , at 0; for x < 0,
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