If fx - -xm- n- N is an even function- then m is

The correct option is B Even integerGiven, f(x) = √(x^m), nϵ N is an even function,where mϵ I . ⇒ f(x) = f( x) ⇒√(x^m) = √(( x)^m) ⇒ x^m = ...

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Byju's Answer

Standard XII

Mathematics

Greatest Binomial Coefficients

If fx = √xm...

Question

If $f (x) = \sqrt[n]{x^{m}}, n ϵ N$ is an even function, then $m$ is

Even integer

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Odd integer

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Any integer

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f (x)

even is not possible

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Solution

The correct option is B Even integer
Given, $f (x) = \sqrt[n]{x^{m}}, n ϵ N$ is an even function,
where $m ϵ I$ .
$\Rightarrow f (x) = f (- x) \Rightarrow \sqrt[n]{x^{m}} = \sqrt[n]{(- x)^{m}}$
$\Rightarrow x^{m} = (- x)^{m}$
$\Rightarrow m$ is an even integer.
Therefore, $m = 2 k, k ϵ I$ .

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If f(x)=n√xm,nϵN is an even function, then m is

The correct option is B Even integerGiven, f(x)=n√xm,nϵN is an even function,where mϵI.⇒f(x)=f(−x)⇒n√xm=n√(−x)m⇒xm=(−x)m⇒m is an even integer.Therefore, m=2k,kϵI.

If $f (x) = \sqrt[n]{x^{m}}, n ϵ N$ is an even function, then $m$ is

The correct option is B Even integer
Given, $f (x) = \sqrt[n]{x^{m}}, n ϵ N$ is an even function,
where $m ϵ I$ .
$\Rightarrow f (x) = f (- x) \Rightarrow \sqrt[n]{x^{m}} = \sqrt[n]{(- x)^{m}}$
$\Rightarrow x^{m} = (- x)^{m}$
$\Rightarrow m$ is an even integer.
Therefore, $m = 2 k, k ϵ I$ .