The function f -0-3- -1-29- defined by f x -2 x 3-15 x 2-36 x -1- isA- One-One and OntoB- Onto but not One-OneC- One-One but not OntoD- Neither One-One nor Onto

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Derivative of One Function w.r.t Another

The function ...

Question

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

One-One and Onto

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Onto but not One-One

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One-One but not Onto

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Neither One-One nor Onto

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Solution

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f : R \to R

f (x) = x^{3} + 2

f : R \to R

f (x) = (x - 1) (x - 2) (x - 3)

\to

$f : R \to R, f (x) = x | x | i s$

$L e t f : [0, \sqrt{3}] \to [0, \frac{π}{3} + l o g_{e} 2] d e f i n e d f (x) = l o g_{e} \sqrt{x^{2} + 1} + t a n^{- 1} x t h e n f (x) i s$

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