Question

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

(a) one-one and onto 

(b) onto but not one-one 

(c) one-one but not onto 

(d) neither one-one not onto 

Answer 1

Correct option (b) onto but not one-one

Explanation:

Given f(x) = 2x³ – 15x² + 36x + 1 

⇒ f'(x) = 6x² – 30x + 36 

⇒ f'(x) = 6(x² – 5x + 6) = 6(x – 2)(x – 3) 

Thus, f'(x) is positive at x < 2 

⇒ f'(x) is negative at 2 < x < 3 

⇒ f'(x) is positive at x > 3

Therefore f(x) is many-one function.

Also, R_f = [1, 29] = Co-domain

Thus f is many-one onto function.