Algebra Examples

$f (x) = 3 x - 4 + 2 x^{2}$

Find $f (- x)$ .

Tap for more steps...

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

$f (- x) = 3 (- x) - 4 + 2 {(- x)}^{2}$

Simplify each term.

Tap for more steps...

Multiply $- 1$ by $3$ .

$f (- x) = - 3 x - 4 + 2 {(- x)}^{2}$

Apply the product rule to $- x$ .

$f (- x) = - 3 x - 4 + 2 ({(- 1)}^{2} x^{2})$

Raise $- 1$ to the power of $2$ .

$f (- x) = - 3 x - 4 + 2 (1 x^{2})$

Multiply $x^{2}$ by $1$ .

$f (- x) = - 3 x - 4 + 2 x^{2}$

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

Tap for more steps...

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

$- 3 x - 4 + 2 x^{2}$ $\neq$ $3 x - 4 + 2 x^{2}$

Since $- 3 x - 4 + 2 x^{2}$ $\neq$ $3 x - 4 + 2 x^{2}$ , the function is not even.

The function is not even

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

Tap for more steps...

Find $- f (x)$ .

Tap for more steps...

Multiply $3 x - 4 + 2 x^{2}$ by $- 1$ .

$- f (x) = - (3 x - 4 + 2 x^{2})$

Apply the distributive property.

$- f (x) = - (3 x) + 4 - (2 x^{2})$

Simplify.

Tap for more steps...

Multiply $3$ by $- 1$ .

$- f (x) = - 3 x + 4 - (2 x^{2})$

Multiply $- 1$ by $- 4$ .

$- f (x) = - 3 x + 4 - (2 x^{2})$

Multiply $2$ by $- 1$ .

$- f (x) = - 3 x + 4 - 2 x^{2}$

Since $- 3 x - 4 + 2 x^{2}$ $\neq$ $- 3 x + 4 - 2 x^{2}$ , the function is not odd.

The function is not odd

The function is neither odd nor even

Enter YOUR Problem