ISRO | ISRO CS 2017 | Question 9

The function f: [0,3]→[1,29] defined by f(x) = 2x³ – 15x² + 36x + 1 is

(A) injective and surjective
(B) surjective but not injective
(C) injective but not surjective
(D) neither injective nor surjective


Answer: (B)

Explanation: Given,
f(x) = 2x³ – 15x² + 36x + 1
⇒ f′(x) = 6(x² − 5x + 6) = 6(x-2)(x-3)

Since f(x) is non monotonic in ∈ [0,3]
⇒ f(x) is not one-one

And, f(x) is increasing in x ∈[0,2) and decreasing in ∈(0,2]
f(0) = 1, f(2) = 29 & f(3) = 28

Therefore Range of f(x) is [1,29]
⇒ f(x) is onto.

So, option (B) is correct.

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