If f(x) = x + a for x 0 and |x − 4| for x > 0, and g(x) = x + 1 for x < 0 and (x - 4)^ 2 + b for x 0, are continuous on R, then (g∘f)(2) + (f∘g)(−2) is equal to

JEE Main 2022 Mathematics question

If f(x) = x + a for and |x − 4| for x > 0, and g(x) = x + 1 for x < 0 and for , are continuous on R, then (g∘f)(2) + (f∘g)(−2) is equal to

Answer: (4)

Continuity of f at 0 gives a = 4, and continuity of g at 0 gives 1 = 16 + b, i.e. b = −15. Then (g∘f)(2) =

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Question ID VK-025171