Answer:
Option B
Explanation:
Concept Involved To check nature of the function
(i) One-One To check one-one, we must check whether
$f'(x) >0$ or $f'(x) <0$ in given domain
(ii) Onto To check onto, we must check
Range = Co-domain
Description of Situation To find range in given domain [a,b] put f'(x)=0 and find $x= \alpha_{1},\alpha_{2},......\alpha_{n}\epsilon[a,b]$
Now find,
{$f(a),f(\alpha_{1}),f(\alpha_{2}),.....f(\alpha_{n}),f(b)}$}
its the greatest and least gives you range.
$f:[0,3] \rightarrow [1,29]$
$f(x)=2x^{3}-15x^{2}+36x+1$
$\therefore$ $f'(x)=6x^{2}-30x+36$
=$6(x^{2}-5x+6)=6(x-2)(x-3)$
For given domain [0,3] ,f(x) is increasing as well as decreasing
$\Rightarrow$ many-one
Now, put $f'(x)=0 \Rightarrow x=2,3$
Thus, for range f(0)=1
f(2)=29,f(3)=28
$\Rightarrow$ Range $\epsilon[1,29]$ $ \therefore$ onto