The odd extension of the function y = $x^{2}$ is y = $- x^{2}$

True

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False

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Solution

The correct option is B
False

We define odd extension or even extension by extending the domain of the function and defining the function for the extended part. The given function $x^{2}$ is an even function and it is defined for all real values of x. So we can not further extend the domain to make it odd.

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Similar questions

The odd extension of the function y = $x^{2}$ is y = $- x^{2}$

Find the odd and even extensions of f(x) = $x^{4} - x^{3} + x^{2}$ (x > 0)

[ Assume the domain and range is x < 0 of the following function ]

y = \frac{x^{2}}{1 + x^{2}}

(x^{2} - y^{2})

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