If the real-valued function f(x) = x^3 + 3(a^2 - 1)x + 1 be invertible then the set of possible real values of a is

JEE Advanced Mathematics question

If the real-valued function be invertible then the set of possible real values of is

(A)
(B)
(C)
(D)Correct

Answer: (D)

Solution

A cubic is onto automatically; it is invertible iff it is one-one, i.e. strictly monotonic. Here . - cannot be decreasing everywhere, since as (leading coefficient ). - is increasing iff $ + - 1

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Question ID VK-110348