Find f(g(x)) f(x)=9x-2 g(x)=-x+3

$f (x) = 9 x - 2$ $g (x) = - x + 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- x + 3)$ by substituting in the value of $g$ into $f$ .

$f (- x + 3) = 9 (- x + 3) - 2$

Step 3

Simplify each term.

Apply the distributive property.

$f (- x + 3) = 9 (- x) + 9 \cdot 3 - 2$

Multiply $- 1$ by $9$ .

$f (- x + 3) = - 9 x + 9 \cdot 3 - 2$

Multiply $9$ by $3$ .

$f (- x + 3) = - 9 x + 27 - 2$

Step 4

Subtract $2$ from $27$ .

$f (- x + 3) = - 9 x + 25$