Find f(g(x)) f(x)=3x+4 g(x)=4x-3

$f (x) = 3 x + 4$ $g (x) = 4 x - 3$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x - 3)$ by substituting in the value of $g$ into $f$ .

$f (4 x - 3) = 3 (4 x - 3) + 4$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x - 3) = 3 (4 x) + 3 \cdot - 3 + 4$

Multiply $4$ by $3$ .

$f (4 x - 3) = 12 x + 3 \cdot - 3 + 4$

Multiply $3$ by $- 3$ .

$f (4 x - 3) = 12 x - 9 + 4$

Step 4

Add $- 9$ and $4$ .

$f (4 x - 3) = 12 x - 5$