Solve the Function Operation f(x)=4-x , f(x+h)-f(x)

$f (x) = 4 - x$ , $f (x + h) - f (x)$

Step 1

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

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

Step 2

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

$(4 - (x + h)) - (4 - x)$

Step 3

Simplify $(4 - (x + h)) - (4 - x)$ .

Simplify each term.

Apply the distributive property.

$4 - x - h - (4 - x)$

Apply the distributive property.

$4 - x - h - 1 \cdot 4 - - x$

Multiply $- 1$ by $4$ .

$4 - x - h - 4 - - x$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$4 - x - h - 4 + 1 x$

Multiply $x$ by $1$ .

$4 - x - h - 4 + x$

Combine the opposite terms in $4 - x - h - 4 + x$ .

Subtract $4$ from $4$ .

$- x - h + 0 + x$

Add $- x - h$ and $0$ .

$- x - h + x$

Add $- x$ and $x$ .

$- h + 0$

Add $- h$ and $0$ .

$- h$