JEE Advanced2012MathematicsFunctionsActual

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

Options

Aone-one and onto
Bonto but not one-one
Cone-one but not onto
Dneither one-one nor onto

Correct answer

B. onto but not one-one

Step-by-step solution

Given : f(x)=2 x³-15 x²+36 x+1 f^ (x)=6 x²-30 x+36=6 (x²-5 x+6 )=6(x-2)(x-3) f^ (x)>0 x [0,2) and f^ (x) < 0 x (2,3) f(x) is increasing on [0,2) and decreasing on (2,3) f(x) is many one on [0,3] Also f(0)=1, f(2)=29, f(3)=28 Absolute min =1 and Absolute max =29 Range of f=[1,29]= codomain Hence f is onto.

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