How do you know if $(3x) / (4-x^2)$ is an even or odd function?

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Answer 1 · 2016-09-14T05:42:50

$(3x)/(4-x^2)$ is an odd function.

A function $f(x))$ is even if $f(-x)=f(x)$ and is odd if $f(-x)=-f(x)$ .

It is also possible that it is neither.

As here $f(x)=(3x)/(4-x^2)$

$f(-x)=(3xx(-x))/(4-(-x)^2)$

= $(-3x)/(4-x^2)$

= $-(3x)/(4-x^2)$

= $-f(x)$

Hence $(3x)/(4-x^2)$ is an odd function.

How do you know if (3x) / (4-x^2) (3x) / (4-x^2) is an even or odd function?