The function f : [0, 3] \rightarrow [1, 29], defined by f(x) = 2x3

Engineering

Mathematics

Classification of Functions

Question

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

onto but not one‑one.

one‑one but not onto.

one‑one and onto.

neither one‑one nor onto.

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$∵$ f(x) = 2x³ – 15x² + 36x + 1

$\Rightarrow$ f '(x) = 6x² – 30x + 36 = 6 (x – 2) (x – 3)

$∵$ sign of f ' changes in [0 3]

$∴$ function is not one‑one

$∵$ f(0) = 1 ; f(2) = 29 and f(3) = 28

$∴$ Range = [1, 29]

$∴$ Function is onto but not one‑one.