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Finite Math Examples

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

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

Step 1

Simplify.

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Step 1.1

Add

x

$x$ and

3 x

$3 x$ .

f (x) = 4 x - 4 + 5

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

Step 1.2

Add

- 4

$- 4$ and

5

$5$ .

f (x) = 4 x + 1

$f (x) = 4 x + 1$

f (x) = 4 x + 1

$f (x) = 4 x + 1$

Step 2

Find

f (- x)

$f (- x)$ .

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Step 2.1

Find

f (- x)

$f (- x)$ by substituting

- x

$- x$ for all occurrence of

x

$x$ in

f (x)

$f (x)$ .

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

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

Step 2.2

Multiply

- 1

$- 1$ by

4

$4$ .

f (- x) = - 4 x + 1

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

f (- x) = - 4 x + 1

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

Step 3

A function is even if

f (- x) = f (x)

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

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Step 3.1

Check if

f (- x) = f (x)

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

Step 3.2

Since

- 4 x + 1

$- 4 x + 1$

\neq

$\neq$

4 x + 1

$4 x + 1$ , the function is not even.

The function is not even

The function is not even

Step 4

A function is odd if

f (- x) = - f (x)

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

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Step 4.1

Find

- f (x)

$- f (x)$ .

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Step 4.1.1

Multiply

4 x + 1

$4 x + 1$ by

- 1

$- 1$ .

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

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

Step 4.1.2

Apply the distributive property.

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

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

Step 4.1.3

Multiply.

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Step 4.1.3.1

Multiply

4

$4$ by

- 1

$- 1$ .

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

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

Step 4.1.3.2

Multiply

- 1

$- 1$ by

1

$1$ .

- f (x) = - 4 x - 1

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

- f (x) = - 4 x - 1

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

- f (x) = - 4 x - 1

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

Step 4.2

Since

- 4 x + 1

$- 4 x + 1$

\neq

$\neq$

- 4 x - 1

$- 4 x - 1$ , the function is not odd.

The function is not odd

The function is not odd

Step 5

The function is neither odd nor even

Step 6

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$