A) one-one and onto
B) onto but not one-one
C) one-one but not onto
D) neither one-one nor onto
Correct Answer: B
Solution :
We have, \[f\left( x \right)=2{{x}^{3}}-15{{x}^{2}}+36x+1\] \[\Rightarrow f'\left( x \right)=6{{x}^{2}}-30x+36\] \[\Rightarrow f'\left( x \right)=6\left( x-2 \right)\left( x-3 \right)\] f(x) is increasing in [0, 2] and decreasing in [2, 3]. f (x) is many one \[f\left( 0 \right)=1,f\left( 2 \right)=29,f\left( 3 \right)=28\] Range = [1, 29] f(x) is onto but not one-one.
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