Find @FORMULA f(x)=7x+11

$f (x) = 7 x + 11$

Step 1

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 2

Find the components of the definition.

Evaluate the function at $x = x + h$ .

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

$f (x + h) = 7 (x + h) + 11$

Simplify the result.

Apply the distributive property.

$f (x + h) = 7 x + 7 h + 11$

The final answer is $7 x + 7 h + 11$ .

$7 x + 7 h + 11$

Reorder $7 x$ and $7 h$ .

$7 h + 7 x + 11$

Find the components of the definition.

$f (x + h) = 7 h + 7 x + 11$

$f (x) = 7 x + 11$

$f (x + h) = 7 h + 7 x + 11$

$f (x) = 7 x + 11$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{7 h + 7 x + 11 - (7 x + 11)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{7 h + 7 x + 11 - (7 x) - 1 \cdot 11}{h}$

Multiply $7$ by $- 1$ .

$\frac{7 h + 7 x + 11 - 7 x - 1 \cdot 11}{h}$

Multiply $- 1$ by $11$ .

$\frac{7 h + 7 x + 11 - 7 x - 11}{h}$

Subtract $7 x$ from $7 x$ .

$\frac{7 h + 0 + 11 - 11}{h}$

Add $7 h$ and $0$ .

$\frac{7 h + 11 - 11}{h}$

Subtract $11$ from $11$ .

$\frac{7 h + 0}{h}$

Add $7 h$ and $0$ .

$\frac{7 h}{h}$

Divide $7$ by $1$ .

$7$

Step 5