Finite Math Examples

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

Step 1

Add $2$ and $1$ .

$f (x) = \frac{\sqrt{x}}{x^{3}}$

Step 2

Find $f (- x)$ .

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Step 2.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = \frac{\sqrt{- x}}{{(- x)}^{3}}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Apply the product rule to $- x$ .

$f (- x) = \frac{\sqrt{- x}}{{(- 1)}^{3} x^{3}}$

Step 2.2.2

Raise $- 1$ to the power of $3$ .

$f (- x) = \frac{\sqrt{- x}}{- x^{3}}$

Step 2.3

Move the negative in front of the fraction.

$f (- x) = - \frac{\sqrt{- x}}{x^{3}}$

Step 3

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

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Step 3.1

Check if $f (- x) = f (x)$ .

Step 3.2

Since $- \frac{\sqrt{- x}}{x^{3}}$ $\neq$ $\frac{\sqrt{x}}{x^{3}}$ , the function is not even.

The function is not even

Step 4

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

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Step 4.1

Multiply $- 1$ by $\frac{\sqrt{x}}{x^{3}}$ .

$- f (x) = - \frac{\sqrt{x}}{x^{3}}$

Step 4.2

Since $- \frac{\sqrt{- x}}{x^{3}}$ $\neq$ $- \frac{\sqrt{x}}{x^{3}}$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6