Calculus Examples

$f (x) = x + 3 x - 4 + 5$

Find $f (- x)$ .

Tap for more steps...

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

$f (- x) = (- x) + 3 (- x) - 4 + 5$

Multiply $- 1$ by $3$ .

$f (- x) = - x - 3 x - 4 + 5$

Subtract $3 x$ from $- x$ .

$f (- x) = - 4 x - 4 + 5$

Add $- 4$ and $5$ .

$f (- x) = - 4 x + 1$

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

Tap for more steps...

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

$- 4 x + 1$ $\neq$ $x + 3 x - 4 + 5$

Since $- 4 x + 1$ $\neq$ $x + 3 x - 4 + 5$ , 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 $x + 3 x - 4 + 5$ by $- 1$ .

$- f (x) = - (x + 3 x - 4 + 5)$

Add $x$ and $3 x$ .

$- f (x) = - (4 x - 4 + 5)$

Add $- 4$ and $5$ .

$- f (x) = - (4 x + 1)$

Apply the distributive property.

$- f (x) = - (4 x) - 1 \cdot 1$

Multiply.

Tap for more steps...

Multiply $4$ by $- 1$ .

$- f (x) = - 4 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- f (x) = - 4 x - 1$

Since $- 4 x + 1$ $\neq$ $- 4 x - 1$ , the function is not odd.

The function is not odd

The function is neither odd nor even

Enter YOUR Problem