Find f(g(x)) f(x)=-6x+3 , g(x)=2x+5

$f (x) = - 6 x + 3$ , $g (x) = 2 x + 5$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x + 5)$ by substituting in the value of $g$ into $f$ .

$f (2 x + 5) = - 6 (2 x + 5) + 3$

Step 3

Simplify each term.

Apply the distributive property.

$f (2 x + 5) = - 6 (2 x) - 6 \cdot 5 + 3$

Multiply $2$ by $- 6$ .

$f (2 x + 5) = - 12 x - 6 \cdot 5 + 3$

Multiply $- 6$ by $5$ .

$f (2 x + 5) = - 12 x - 30 + 3$

Step 4

Add $- 30$ and $3$ .

$f (2 x + 5) = - 12 x - 27$