Calculus Examples

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

Step 1

Simplify.

Tap for more steps...

Step 1.1

Add $x$ and $3 x$ .

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

Step 1.2

Add $- 4$ and $5$ .

$f (x) = 4 x + 1$

Step 2

Find $f (- x)$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Multiply $- 1$ by $4$ .

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

Step 3

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

Tap for more steps...

Step 3.1

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

Step 3.2

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

The function is not even

Step 4

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

Tap for more steps...

Step 4.1

Find $- f (x)$ .

Tap for more steps...

Step 4.1.1

Multiply $4 x + 1$ by $- 1$ .

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

Step 4.1.2

Apply the distributive property.

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

Step 4.1.3

Multiply.

Tap for more steps...

Step 4.1.3.1

Multiply $4$ by $- 1$ .

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

Step 4.1.3.2

Multiply $- 1$ by $1$ .

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

Step 4.2

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

The function is not odd

Step 5

The function is neither odd nor even

Step 6

Enter YOUR Problem