**47. ** The function f : [0, 3] [1, 29], defined by f(x) = 2x ^{ 3 } 15x ^{ 2 } + 36x + 1, is

(A) one-one and onto (B) onto but not one-one

(C) one-one but not onto (D) neither one-one nor onto

the given function is

differentiating the function wrt x,

thus the function is increasing from 0<x<2,

and then decreasing from x=2 to x=3

it is not monotonically increasing or decreasing.

thus the function is not one-one.

now we will check the image of the function at critical points.

therefore the function is onto, but not one-one.

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