IIT-JEE 2012 · Paper 1 · Mathematics Q43

MathematicsSingle correct+3 / -1Question 43 of 60

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

one-one and onto.

onto but not one-one.

one-one but not onto.

neither one-one nor onto.

Answer and worked solution

Official answer: B

Monotonicity. $f'(x)=6x^2-30x+36=6(x-2)(x-3)$ : increasing on $[0,2]$ , decreasing on $[2,3]$ .

Values. $f(0)=1$ , $f(2)=29$ , $f(3)=28$ . The range is $[1,29]$ , so $f$ is onto.

Not one-one. Every value in $[28,29)$ is taken once on $(0,2)$ and once on $(2,3]$ .

(B)

Topics:Types of functions Monotonicity

IIT-JEE 2012 · Paper 1, Mathematics question 43