Chapter 2: Q. 21 (page 124)

Determine(algebraically) whethere the given function is even, odd,or neither.
$f (x) = \frac{x}{1 + x^{2}}$

Short Answer

Expert verified

The given function $f (x) = \frac{x}{1 + x^{2}}$ is odd function

Step by step solution

Step 1.Given information

The given function $f (x) = \frac{x}{1 + x^{2}}$

Step 2.Determine the given function is even,odd or neither.

The function is even if $f (- x) = f (x)$ and odd if $f (- x) = f (- x)$ .If none of these conditions are satisfied.

Find $f (- x)$ by replacing -x for x in the given function.

$f (- x) = \frac{- x}{1 + {(- x)}^{2}} = \frac{- x}{1 + x^{2}} = - (\frac{x}{1 + x^{2}}) = - f (x)$

Therefore,the given function is odd since $f (- x) = - f (x)$

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Determine(algebraically) whethere the given function is even, odd,or neither.
$f (x) = \frac{x}{1 + x^{2}}$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Determine the given function is even,odd or neither.

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Determine(algebraically) whethere the given function is even, odd,or neither.f(x)=x1+x2

Short Answer

Step by step solution

Step 1.Given information

Step 2.Determine the given function is even,odd or neither.

One App. One Place for Learning.

Most popular questions from this chapter

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Determine(algebraically) whethere the given function is even, odd,or neither.
$f (x) = \frac{x}{1 + x^{2}}$