Precalculus Examples

$f (x) = 7 x^{\frac{3}{4}}$

Step 1

Find $f (- x)$ .

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Step 1.1

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

$f (- x) = 7 {(- x)}^{\frac{3}{4}}$

Step 1.2

Apply the product rule to $- x$ .

$f (- x) = 7 {(- 1)}^{\frac{3}{4}} x^{\frac{3}{4}}$

Step 2

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

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Step 2.1

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

Step 2.2

Since $7 {(- 1)}^{\frac{3}{4}} x^{\frac{3}{4}}$ $\neq$ $7 x^{\frac{3}{4}}$ , the function is not even.

The function is not even

Step 3

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

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Step 3.1

Multiply $7$ by $- 1$ .

$- f (x) = - 7 x^{\frac{3}{4}}$

Step 3.2

Since $7 {(- 1)}^{\frac{3}{4}} x^{\frac{3}{4}}$ $\neq$ $- 7 x^{\frac{3}{4}}$ , the function is not odd.

The function is not odd

Step 4

The function is neither odd nor even

Step 5