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
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.
Quiz of this Question
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.