Finite Math Examples

$f (x) = 8 x - 5$ , $f (x + h) - f (x)$

Step 1

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = 8 (x + h) - 5$

Step 2

Replace the function designators in $f (x + h) - f (x)$ with the actual functions.

$(8 (x + h) - 5) - (8 x - 5)$

Step 3

Simplify $(8 (x + h) - 5) - (8 x - 5)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$8 x + 8 h - 5 - (8 x - 5)$

Step 3.1.2

Apply the distributive property.

$8 x + 8 h - 5 - (8 x) - - 5$

Step 3.1.3

Multiply $8$ by $- 1$ .

$8 x + 8 h - 5 - 8 x - - 5$

Step 3.1.4

Multiply $- 1$ by $- 5$ .

$8 x + 8 h - 5 - 8 x + 5$

Step 3.2

Combine the opposite terms in $8 x + 8 h - 5 - 8 x + 5$ .

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Step 3.2.1

Subtract $8 x$ from $8 x$ .

$8 h - 5 + 0 + 5$

Step 3.2.2

Add $8 h - 5$ and $0$ .

$8 h - 5 + 5$

Step 3.2.3

Add $- 5$ and $5$ .

$8 h + 0$

Step 3.2.4

Add $8 h$ and $0$ .

$8 h$