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

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Answer 1 · 2016-09-14T05:42:50

$\frac{3 x}{4 - x^{2}}$ $(3x)/(4-x^2)$ is an odd function.

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

It is also possible that it is neither.

As here $f (x) = \frac{3 x}{4 - x^{2}}$ $f(x)=(3x)/(4-x^2)$

$f (- x) = \frac{3 \times (- x)}{4 - {(- x)}^{2}}$ $f(-x)=(3xx(-x))/(4-(-x)^2)$

= $\frac{- 3 x}{4 - x^{2}}$ $(-3x)/(4-x^2)$

= $- \frac{3 x}{4 - x^{2}}$ $-(3x)/(4-x^2)$

= $- f (x)$ $-f(x)$

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

How do you know if (3x) / (4-x^2) 3x4−x2(3x) / (4-x^2) is an even or odd function?