If f x is defined in - a - b - where a - b - 0- then find the even extension of f x -

To get even extension replace x by x, i.e. f(x), here x ∈ [a, b] ⇒ x ∈ [ b, a] ⇒ domain [To understand how we get domain, we can consider the function √(x). ...

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Standard X

Mathematics

Nth Term of a GP

If f x is def...

Question

If f(x) is defined in [a, b] where a,b $\geq$ 0, then find the even extension of f(x).

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Solution

To get even extension replace x by -x, i.e. f(x), here x $\in$ [a, b]

$\Rightarrow$ -x $\in$ [ -b,-a] $\Rightarrow$ domain

[To understand how we get domain, we can consider the function $\sqrt{x}$ . $\sqrt{x}$ is defined for x $>$ 0, whereas the even extension of $\sqrt{x}$ , $\sqrt{- x}$ is not defined when x $l t$ 0]

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If f(x) is defined in [a, b] where a,b ≥ 0, then find the even extension of f(x).

To get even extension replace x by -x, i.e. f(x), here x ∈ [a, b] ⇒ -x ∈ [ -b,-a] ⇒ domain [To understand how we get domain, we can consider the function √x. √x is defined for x > 0, whereas the even extension of √x, √−x is not defined when x lt0]

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