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Question

The function f: given by fx=x3-1 is


A

a One-One function.

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B

an Onto function.

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C

a Bijection

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D

neither One-One nor Onto

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Solution

The correct option is C

a Bijection


The explanation for the correct option

Given function, fx=x3-1.

Differentiate the given function with respect to x.

ddxfx=ddxx3-1f'x=ddxx3+ddx-1ddx(u±v)=dudx±dvdxf'x=3x2+0f'x=3x2

As 3x2 is always non-negative, so f'x0.

Thus, the given function is always increasing.

Hence, the given function is a One-One function.

As the given function is a polynomial function, thus it is defined for all real values of x and the range is also all real numbers.

Thus, the range is , which is equal to the given co-domain.

Hence, the given function is an Onto function.

So, the given function is a bijection.

Hence, the correct option is OptionC


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